F5030 Introduction to Quantum Mechanics

Faculty of Science
autumn 2021
Extent and Intensity
3/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught partially online.
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Dominik Munzar, Dr.
Department of Condensed Matter Physics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Condensed Matter Physics - Physics Section - Faculty of Science
Prerequisites
F4120 Theoretical mechanics || F4050 Introduction to Microphysics
Basic university level course of physics.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
This is an introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Learning outcomes
After passing the course the students should be able to:
- formulate simple physical problems on the quantum mechanical level
- solve the formulated problems using Schrodinger equation and/or its approximations
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discreteness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
https://www.physics.muni.cz/~chaloupka/F5030/
www pages related to the previous course taught by Prof. Tyc: http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2020
Extent and Intensity
3/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught partially online.
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Dominik Munzar, Dr.
Department of Condensed Matter Physics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Condensed Matter Physics - Physics Section - Faculty of Science
Timetable
Thu 12:00–14:50 F1,01014
  • Timetable of Seminar Groups:
F5030/01: Mon 10:00–11:50 F4,03017
Prerequisites
F4120 Theoretical mechanics || F4050 Introduction to Microphysics
Basic university level course of physics.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
This is an introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Learning outcomes
After passing the course the students should be able to:
- formulate simple physical problems on the quantum mechanical level
- solve the formulated problems using Schrodinger equation and/or its approximations
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discreteness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
https://www.physics.muni.cz/~chaloupka/F5030/
www pages related to the previous course taught by Prof. Tyc: http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2019
Extent and Intensity
3/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Dominik Munzar, Dr.
Department of Condensed Matter Physics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Condensed Matter Physics - Physics Section - Faculty of Science
Timetable
Thu 12:00–14:50 F1,01014
  • Timetable of Seminar Groups:
F5030/01: Fri 8:00–9:50 F1,01014
Prerequisites
F4120 Theoretical mechanics || F4050 Introduction to Microphysics
Basic university level course of physics.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
This is an introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Learning outcomes
After passing the course the students should be able to:
- formulate simple physical problems on the quantum mechanical level
- solve the formulated problems using Schrodinger equation and/or its approximations
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discreteness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2018
Extent and Intensity
3/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Dominik Munzar, Dr.
Department of Condensed Matter Physics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Condensed Matter Physics - Physics Section - Faculty of Science
Timetable
Mon 17. 9. to Fri 14. 12. Thu 12:00–14:50 F1,01014
  • Timetable of Seminar Groups:
F5030/01: Mon 17. 9. to Fri 14. 12. Fri 8:00–9:50 F1,01014
Prerequisites (in Czech)
F4120 Theoretical mechanics || F4050 Introduction to Microphysics
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discreteness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
autumn 2017
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Dominik Munzar, Dr.
Department of Condensed Matter Physics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Condensed Matter Physics - Physics Section - Faculty of Science
Timetable
Mon 18. 9. to Fri 15. 12. Thu 12:00–13:50 F1,01014, Fri 8:00–9:50 F4,03017
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discreteness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2016
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Timetable
Mon 19. 9. to Sun 18. 12. Wed 8:00–9:50 F4,03017, Thu 12:00–13:50 F1,01014
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discreteness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2015
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Timetable
Thu 11:00–12:50 F3,03015, Thu 13:00–14:50 F3,03015
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discreteness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2014
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Timetable
Thu 13:00–14:50 F1,01014, Fri 10:00–11:50 F3,03015
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discreteness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2013
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Timetable
Mon 15:00–16:50 F1,01014, Thu 13:00–14:50 F3,03015
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discreteness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2012
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Supplier department: Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Timetable
Tue 15:00–16:50 F2,02012, Thu 14:00–15:50 F3,03015
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discretness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2011
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Timetable
Thu 13:00–14:50 F3,03015, Fri 8:00–9:50 F4,03017
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 13 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discretness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2010
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Timetable
Thu 13:00–14:50 F1,01014
  • Timetable of Seminar Groups:
F5030/01: Fri 8:00–9:50 F3,03015
F5030/02: Thu 15:00–16:50 Fs1,01017
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discretness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2009
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Timetable
Thu 16:00–17:50 F3,03015
  • Timetable of Seminar Groups:
F5030/01: Thu 8:00–9:50 F1,01014
F5030/02: Wed 12:00–13:50 Fs1,01017
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations; to learn about identical particles and basics of quantum information (entangled states, quantum cryptography, quantum teleportation and cloning).
Syllabus
  • Motivation for quantum mechanics (unusual behaviour of small objects, insufficiency of classical mechanics and the need of quantum mechanics, applications in technology, chemical bond, consequences for human life).
  • Connection between classical and quantum mechanics and its analogy with connection between geometrical and wave optics.
  • The concept of probability amplitude and wavefunction (event and its probability amplitude, superposition principle, wavefunction as the probability amplitude of finding a particle at a given point).
  • Hilbert space, quantum states and operators, scalar product and its physical meaning, physical quantities as Hermitian operators, expectation values of operators.
  • Coordinate representation (states of a particle on a line, wavefunction, position operator and its eigenstates, Dirac delta function, momentum operator, transition between coordinate and momentum representations).
  • Uncertainty relations (their derivation in general, application to position and momentum and to angular momentum components, wave packets).
  • Schroedinger equation (Hamilton operator, stationary states, time evolution of a general state).
  • One-dimensional problems (discrete and continuous spectrum of energy, reflection on a potential barrier, well and step, tunneling effect).
  • Harmonic oscillator (algebraic approach, creation and annihilation operator, energy spectrum, applications - photons, phonons, Planck radiation law).
  • Angular momentum (non-commutativity of 3D rotations and components of angular momentum, ladder operators, integer and half-integer angular momentum, spin).
  • Hydrogen atom (separation of variables in spherical coordinates, solution of the angular and radial parts, energy eigenvalues, degeneracy).
  • Approximative methods (stationary non-degenerate, degenerate and non-stationary perturbation theory, probability of transition, Fermi golden rule, variation method and its applications).
  • Identical particles (change of state under permutation of particles, bosons and fermions, Slater determinant, Pauli principle, Fermi energy).
  • Basics of quantum information (quantum entanglement, Bell states, measurement and state collapse, very briefly quantum cryptography, teleportation, cloning and quantum computers).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
Teaching methods
2 hours of lecture + 2 hours of tutorials per week. The lecture presents the theory and the tutorials are devoted to exercising the theory by solving problems.
Assessment methods
Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2008
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Timetable
Thu 12:00–13:50 F3,03015, Thu 14:00–15:50 Fs1,01017
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations; to learn about identical particles and basics of quantum information (entangled states, quantum cryptography, quantum teleportation and cloning).
Syllabus
  • Motivation for quantum mechanics (unusual behaviour of small objects, insufficiency of classical mechanics and the need of quantum mechanics, applications in technology, chemical bond, consequences for human life).
  • Connection between classical and quantum mechanics and its analogy with connection between geometrical and wave optics.
  • The concept of probability amplitude and wavefunction (event and its probability amplitude, superposition principle, wavefunction as the probability amplitude of finding a particle at a given point).
  • Hilbert space, quantum states and operators, scalar product and its physical meaning, physical quantities as Hermitian operators, expectation values of operators.
  • Coordinate representation (states of a particle on a line, wavefunction, position operator and its eigenstates, Dirac delta function, momentum operator, transition between coordinate and momentum representations).
  • Uncertainty relations (their derivation in general, application to position and momentum and to angular momentum components, wave packets).
  • Schroedinger equation (Hamilton operator, stationary states, time evolution of a general state).
  • One-dimensional problems (discrete and continuous spectrum of energy, reflection on a potential barrier, well and step, tunneling effect).
  • Harmonic oscillator (algebraic approach, creation and annihilation operator, energy spectrum, applications - photons, phonons, Planck radiation law).
  • Angular momentum (non-commutativity of 3D rotations and components of angular momentum, ladder operators, integer and half-integer angular momentum, spin).
  • Hydrogen atom (separation of variables in spherical coordinates, solution of the angular and radial parts, energy eigenvalues, degeneracy).
  • Approximative methods (stationary non-degenerate, degenerate and non-stationary perturbation theory, probability of transition, Fermi golden rule, variation method and its applications).
  • Identical particles (change of state under permutation of particles, bosons and fermions, Slater determinant, Pauli principle, Fermi energy).
  • Basics of quantum information (quantum entanglement, Bell states, measurement and state collapse, very briefly quantum cryptography, teleportation, cloning and quantum computers).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
Assessment methods
Final examination has both written and oral parts. Home work is required during semester. To be able to sit for the examination, the student must gather enough credits that can be obtained for home work and for written tests during semester.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2007
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Timetable
Mon 14:00–15:50 F4,03017
  • Timetable of Seminar Groups:
F5030/01: Mon 16:00–17:50 F4,03017
F5030/02: Tue 9:00–10:50 F2,02012
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Basic course in nonrelativistic quantum mechanics. The probability amplitude and wavefuction. Formalism of quantum mechanics: mathematical tools, postulates, Schrödinger equation. One-dimensional problems - potential steps and barriers, tunneling. Quantization of a harmonic oscillator, angular momentum and of the hydrogen atom. Spin 1/2, Pauli matrices. Systems of identical particles. Approximative methods - time independent and dependent perturbation theory, Fermi golden rule, variational method. Density matrix, entangled states, Bell inequalities, Greenberger-Horne-Zeilinger states. Note on quantum cryptography, teleportation, cloning, and quantum computers.
Syllabus (in Czech)
  • 1. Motivace pro kvantovou mechaniku - neobvyklé chování kvantových objektů - úspěšnost kvantové fyziky při vysvětlení jevů týkajících se malých objektů - nezbytnost kvantové mechaniky pro pochopení i těch nejzákladnějších vlastností hmoty - aplikace v technologiích (počítače, mobilní telefony, nové materiály atd.) - chemická vazba - nelze porozumět bez kvantové mechaniky, podobně procesy v živé přírodě 2. Analogie geometrická vs. vlnová optika -- klasická vs. kvantová mechanika - trajektorie světelného paprsku daná Fermatovým principem - šíření světla po všech možných trajektoriích podle Huygensova-Fresnelova principu - trajektorie hmotného bodu daná Hamiltonovým principem - šíření hmotného po všech možných trajektoriích ve shodě s Feynmanovou formulací kvantové mechaniky 3. Pojem amplitudy pravděpodobnosti a vlnové funkce - událost a její amplituda pravděpodobnosti - princip superpozice pro amplitudy pravděpodobnosti, příklady - skládání pravděpodobností v klasické a kvantové mechanice - vlnová funkce - amplituda nalezení částice v daném místě prostoru - normování vlnové funkce 4. Kvantové stavy a operátory - Hilbertův prostor - fyzikální význam skalárního součinu - fyzikální veličiny a hermitovské operátory - možné výsledky měření fyzikální veličiny, spektrum operátoru - ortogonalita vlastních stavů, její fyzikální význam - rozklad jednotkového operátoru - střední hodnota operátoru 5. Souřadnicová reprezentace - stavy částice na přímce, vlnová funkce - operátor souřadnice a jeho vlastní stavy, Diracova delta funkce - operátor hybnosti jako generátor translace, vlastní stavy - komutační relace pro operátor souřadnice a hybnosti - přechod od souřadnicové k impulzové reprezentaci a zpět 6. Obecné relace neurčitosti - odvození relací neurčitosti v obecném tvaru - příklady: operátory souřadnice a hybnosti, složky momentu hybnosti - vlnová klubka, vlastní stavy momentu hybnosti 7. Schrödingerova rovnice - linearita časového vývoje, rovnice prvního řádu - Hamiltonův operátor - stacionární stavy, jejich časový vývoj - časový vývoj pravděpodobností a středních hodnot ve stacionárním stavu - časový vývoj obecného stavu vyjádřeného v bázi stacionárních stavů - hustota toku pravděpodobnosti 8. Jednorozměrné problémy - řešení Schrödingerovy rovnice pro pravoúhlé potenciálové bariéry - diskrétní a spojité spektrum energií v jámě - odraz od bariéry, jámy a schodu - tunelování - příklady (hrot v elektronovém mikroskopu, alfa-rozpad, Josephsonův jev) 9. Harmonický oscilátor - zavedení kreačního a anihilačního operátoru, jejich komutátor - generování nových vlastních stavů hamiltoniánu - omezení energie zdola, spektrum možných hodnot energie - aplikace: fotony, fonony, Planckův vyzařovací zákon 10. Kvantování momentu hybnosti - vlastnosti trojrozměrných rotací, komutační relace pro složky momentu hybnosti - výběr vhodného systému komutujících veličin - žebříčkové operátory, tvoření nových vlastních stavů - celočíselný a poločíselný moment hybnosti, spinový stupeň volnosti - dalekosáhlé důsledky: rotační spektra molekul, stavy elektronů v atomu, výběrová pravidla pro přechod mezi stavy 11. Atom vodíku - přechod do těžišťové soustavy a ke sférickým souřadnicím - rozpad problému na úhlovou a radiální část - úhlová část - převedení na moment hybnosti - řešení radiální části, vlastní hodnoty energie, degenerace hladin 12. Přibližné metody - stacionární poruchová teorie, opravy k energii a koeficienty nových stacionárních stavů - degenerovaný případ, sekulární rovnice - časově proměnné poruchy, pravděpodobnost přechodu, Fermiho zlaté pravidlo - variační metoda a její aplikace v chemii 13. Identické částice - změna stavu při záměně částic - bosony a fermiony - fermiony - Slaterův determinant, Pauliho pincip, Fermiho energie - bosony - bunching, Cooperovy páry 14. Modernejší partie - provázanost (entanglement), Bellovy a GHZ stavy - popis podsystému pomocí matice hustoty - měření a kolaps stavu - Bellovy nerovnosti - zmínka o kvantové kryptografii, teleportaci, klonování a kvantových počítačích.
Literature
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
Assessment methods (in Czech)
Přednáška, cvičení
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2006
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
prof. RNDr. Michal Lenc, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Timetable
Thu 11:00–12:50 F3,03015
  • Timetable of Seminar Groups:
F5030/1: Fri 8:00–9:50 F4,03017, M. Lenc
F5030/2: Fri 12:00–13:50 F3,03015, M. Lenc
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Basic course in nonrelativistic quantum mechanics. The probability amplitude and wavefuction. Formalism of quantum mechanics: mathematical tools, postulates, Schrödinger equation. One-dimensional problems - potential steps and barriers, tunneling. Quantization of a harmonic oscillator, angular momentum and of the hydrogen atom. Spin 1/2, Pauli matrices. Systems of identical particles. Approximative methods - time independent and dependent perturbation theory, Fermi golden rule, variational method. Density matrix, entangled states, Bell inequalities, Greenberger-Horne-Zeilinger states. Note on quantum cryptography, teleportation, cloning, and quantum computers.
Syllabus (in Czech)
  • 1. Motivace pro kvantovou mechaniku - neobvyklé chování kvantových objektů - úspěšnost kvantové fyziky při vysvětlení jevů týkajících se malých objektů - nezbytnost kvantové mechaniky pro pochopení i těch nejzákladnějších vlastností hmoty - aplikace v technologiích (počítače, mobilní telefony, nové materiály atd.) - chemická vazba - nelze porozumět bez kvantové mechaniky, podobně procesy v živé přírodě 2. Analogie geometrická vs. vlnová optika -- klasická vs. kvantová mechanika - trajektorie světelného paprsku daná Fermatovým principem - šíření světla po všech možných trajektoriích podle Huygensova-Fresnelova principu - trajektorie hmotného bodu daná Hamiltonovým principem - šíření hmotného po všech možných trajektoriích ve shodě s Feynmanovou formulací kvantové mechaniky 3. Pojem amplitudy pravděpodobnosti a vlnové funkce - událost a její amplituda pravděpodobnosti - princip superpozice pro amplitudy pravděpodobnosti, příklady - skládání pravděpodobností v klasické a kvantové mechanice - vlnová funkce - amplituda nalezení částice v daném místě prostoru - normování vlnové funkce 4. Kvantové stavy a operátory - Hilbertův prostor - fyzikální význam skalárního součinu - fyzikální veličiny a hermitovské operátory - možné výsledky měření fyzikální veličiny, spektrum operátoru - ortogonalita vlastních stavů, její fyzikální význam - rozklad jednotkového operátoru - střední hodnota operátoru 5. Souřadnicová reprezentace - stavy částice na přímce, vlnová funkce - operátor souřadnice a jeho vlastní stavy, Diracova delta funkce - operátor hybnosti jako generátor translace, vlastní stavy - komutační relace pro operátor souřadnice a hybnosti - přechod od souřadnicové k impulzové reprezentaci a zpět 6. Obecné relace neurčitosti - odvození relací neurčitosti v obecném tvaru - příklady: operátory souřadnice a hybnosti, složky momentu hybnosti - vlnová klubka, vlastní stavy momentu hybnosti 7. Schrödingerova rovnice - linearita časového vývoje, rovnice prvního řádu - Hamiltonův operátor - stacionární stavy, jejich časový vývoj - časový vývoj pravděpodobností a středních hodnot ve stacionárním stavu - časový vývoj obecného stavu vyjádřeného v bázi stacionárních stavů - hustota toku pravděpodobnosti 8. Jednorozměrné problémy - řešení Schrödingerovy rovnice pro pravoúhlé potenciálové bariéry - diskrétní a spojité spektrum energií v jámě - odraz od bariéry, jámy a schodu - tunelování - příklady (hrot v elektronovém mikroskopu, alfa-rozpad, Josephsonův jev) 9. Harmonický oscilátor - zavedení kreačního a anihilačního operátoru, jejich komutátor - generování nových vlastních stavů hamiltoniánu - omezení energie zdola, spektrum možných hodnot energie - aplikace: fotony, fonony, Planckův vyzařovací zákon 10. Kvantování momentu hybnosti - vlastnosti trojrozměrných rotací, komutační relace pro složky momentu hybnosti - výběr vhodného systému komutujících veličin - žebříčkové operátory, tvoření nových vlastních stavů - celočíselný a poločíselný moment hybnosti, spinový stupeň volnosti - dalekosáhlé důsledky: rotační spektra molekul, stavy elektronů v atomu, výběrová pravidla pro přechod mezi stavy 11. Atom vodíku - přechod do těžišťové soustavy a ke sférickým souřadnicím - rozpad problému na úhlovou a radiální část - úhlová část - převedení na moment hybnosti - řešení radiální části, vlastní hodnoty energie, degenerace hladin 12. Přibližné metody - stacionární poruchová teorie, opravy k energii a koeficienty nových stacionárních stavů - degenerovaný případ, sekulární rovnice - časově proměnné poruchy, pravděpodobnost přechodu, Fermiho zlaté pravidlo - variační metoda a její aplikace v chemii 13. Identické částice - změna stavu při záměně částic - bosony a fermiony - fermiony - Slaterův determinant, Pauliho pincip, Fermiho energie - bosony - bunching, Cooperovy páry 14. Modernejší partie - provázanost (entanglement), Bellovy a GHZ stavy - popis podsystému pomocí matice hustoty - měření a kolaps stavu - Bellovy nerovnosti - zmínka o kvantové kryptografii, teleportaci, klonování a kvantových počítačích.
Literature
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
Assessment methods (in Czech)
Přednáška, cvičení
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2005
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
Mgr. Ondřej Přibyla (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Timetable
Mon 18:00–19:50 F4,03017, Tue 12:00–13:50 F3,03015, Thu 12:00–13:50 F1,01014
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Basic course in nonrelativistic quantum mechanics. The probability amplitude and wavefuction. Formalism of quantum mechanics: mathematical tools, postulates, Schrödinger equation. One-dimensional problems - potential steps and barriers, tunneling. Quantization of a harmonic oscillator, angular momentum and of the hydrogen atom. Spin 1/2, Pauli matrices. Systems of identical particles. Approximative methods - time independent and dependent perturbation theory, Fermi golden rule, variational method. Density matrix, entangled states, Bell inequalities, Greenberger-Horne-Zeilinger states. Note on quantum cryptography, teleportation, cloning, and quantum computers.
Syllabus (in Czech)
  • 1. Motivace pro kvantovou mechaniku - neobvyklé chování kvantových objektů - úspěšnost kvantové fyziky při vysvětlení jevů týkajících se malých objektů - nezbytnost kvantové mechaniky pro pochopení i těch nejzákladnějších vlastností hmoty - aplikace v technologiích (počítače, mobilní telefony, nové materiály atd.) - chemická vazba - nelze porozumět bez kvantové mechaniky, podobně procesy v živé přírodě 2. Analogie geometrická vs. vlnová optika -- klasická vs. kvantová mechanika - trajektorie světelného paprsku daná Fermatovým principem - šíření světla po všech možných trajektoriích podle Huygensova-Fresnelova principu - trajektorie hmotného bodu daná Hamiltonovým principem - šíření hmotného po všech možných trajektoriích ve shodě s Feynmanovou formulací kvantové mechaniky 3. Pojem amplitudy pravděpodobnosti a vlnové funkce - událost a její amplituda pravděpodobnosti - princip superpozice pro amplitudy pravděpodobnosti, příklady - skládání pravděpodobností v klasické a kvantové mechanice - vlnová funkce - amplituda nalezení částice v daném místě prostoru - normování vlnové funkce 4. Kvantové stavy a operátory - Hilbertův prostor - fyzikální význam skalárního součinu - fyzikální veličiny a hermitovské operátory - možné výsledky měření fyzikální veličiny, spektrum operátoru - ortogonalita vlastních stavů, její fyzikální význam - rozklad jednotkového operátoru - střední hodnota operátoru 5. Souřadnicová reprezentace - stavy částice na přímce, vlnová funkce - operátor souřadnice a jeho vlastní stavy, Diracova delta funkce - operátor hybnosti jako generátor translace, vlastní stavy - komutační relace pro operátor souřadnice a hybnosti - přechod od souřadnicové k impulzové reprezentaci a zpět 6. Obecné relace neurčitosti - odvození relací neurčitosti v obecném tvaru - příklady: operátory souřadnice a hybnosti, složky momentu hybnosti - vlnová klubka, vlastní stavy momentu hybnosti 7. Schrödingerova rovnice - linearita časového vývoje, rovnice prvního řádu - Hamiltonův operátor - stacionární stavy, jejich časový vývoj - časový vývoj pravděpodobností a středních hodnot ve stacionárním stavu - časový vývoj obecného stavu vyjádřeného v bázi stacionárních stavů - hustota toku pravděpodobnosti 8. Jednorozměrné problémy - řešení Schrödingerovy rovnice pro pravoúhlé potenciálové bariéry - diskrétní a spojité spektrum energií v jámě - odraz od bariéry, jámy a schodu - tunelování - příklady (hrot v elektronovém mikroskopu, alfa-rozpad, Josephsonův jev) 9. Harmonický oscilátor - zavedení kreačního a anihilačního operátoru, jejich komutátor - generování nových vlastních stavů hamiltoniánu - omezení energie zdola, spektrum možných hodnot energie - aplikace: fotony, fonony, Planckův vyzařovací zákon 10. Kvantování momentu hybnosti - vlastnosti trojrozměrných rotací, komutační relace pro složky momentu hybnosti - výběr vhodného systému komutujících veličin - žebříčkové operátory, tvoření nových vlastních stavů - celočíselný a poločíselný moment hybnosti, spinový stupeň volnosti - dalekosáhlé důsledky: rotační spektra molekul, stavy elektronů v atomu, výběrová pravidla pro přechod mezi stavy 11. Atom vodíku - přechod do těžišťové soustavy a ke sférickým souřadnicím - rozpad problému na úhlovou a radiální část - úhlová část - převedení na moment hybnosti - řešení radiální části, vlastní hodnoty energie, degenerace hladin 12. Přibližné metody - stacionární poruchová teorie, opravy k energii a koeficienty nových stacionárních stavů - degenerovaný případ, sekulární rovnice - časově proměnné poruchy, pravděpodobnost přechodu, Fermiho zlaté pravidlo - variační metoda a její aplikace v chemii 13. Identické částice - změna stavu při záměně částic - bosony a fermiony - fermiony - Slaterův determinant, Pauliho pincip, Fermiho energie - bosony - bunching, Cooperovy páry 14. Modernejší partie - provázanost (entanglement), Bellovy a GHZ stavy - popis podsystému pomocí matice hustoty - měření a kolaps stavu - Bellovy nerovnosti - zmínka o kvantové kryptografii, teleportaci, klonování a kvantových počítačích.
Literature
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
Assessment methods (in Czech)
Přednáška, cvičení
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2004
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
prof. RNDr. Michal Lenc, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Timetable
Thu 12:00–13:50 F3,03015, Fri 8:00–9:50 F1,01014
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
Basic course in nonrelativistic quantum mechanics. The probability amplitude and wavefuction. Formalism of quantum mechanics: mathematical tools, postulates, Schrödinger equation. One-dimensional problems - potential steps and barriers, tunneling. Quantization of a harmonic oscillator, angular momentum and of the hydrogen atom. Spin 1/2, Pauli matrices. Systems of identical particles. Approximative methods - time independent and dependent perturbation theory, Fermi golden rule, variational method. Density matrix, entangled states, Bell inequalities, Greenberger-Horne-Zeilinger states. Note on quantum cryptography, teleportation, cloning, and quantum computers.
Syllabus (in Czech)
  • 1. Motivace pro kvantovou mechaniku - neobvyklé chování kvantových objektů - úspěšnost kvantové fyziky při vysvětlení jevů týkajících se malých objektů - nezbytnost kvantové mechaniky pro pochopení i těch nejzákladnějších vlastností hmoty - aplikace v technologiích (počítače, mobilní telefony, nové materiály atd.) - chemická vazba - nelze porozumět bez kvantové mechaniky, podobně procesy v živé přírodě 2. Analogie geometrická vs. vlnová optika -- klasická vs. kvantová mechanika - trajektorie světelného paprsku daná Fermatovým principem - šíření světla po všech možných trajektoriích podle Huygensova-Fresnelova principu - trajektorie hmotného bodu daná Hamiltonovým principem - šíření hmotného po všech možných trajektoriích ve shodě s Feynmanovou formulací kvantové mechaniky 3. Pojem amplitudy pravděpodobnosti a vlnové funkce - událost a její amplituda pravděpodobnosti - princip superpozice pro amplitudy pravděpodobnosti, příklady - skládání pravděpodobností v klasické a kvantové mechanice - vlnová funkce - amplituda nalezení částice v daném místě prostoru - normování vlnové funkce 4. Kvantové stavy a operátory - Hilbertův prostor - fyzikální význam skalárního součinu - fyzikální veličiny a hermitovské operátory - možné výsledky měření fyzikální veličiny, spektrum operátoru - ortogonalita vlastních stavů, její fyzikální význam - rozklad jednotkového operátoru - střední hodnota operátoru 5. Souřadnicová reprezentace - stavy částice na přímce, vlnová funkce - operátor souřadnice a jeho vlastní stavy, Diracova delta funkce - operátor hybnosti jako generátor translace, vlastní stavy - komutační relace pro operátor souřadnice a hybnosti - přechod od souřadnicové k impulzové reprezentaci a zpět 6. Obecné relace neurčitosti - odvození relací neurčitosti v obecném tvaru - příklady: operátory souřadnice a hybnosti, složky momentu hybnosti - vlnová klubka, vlastní stavy momentu hybnosti 7. Schrödingerova rovnice - linearita časového vývoje, rovnice prvního řádu - Hamiltonův operátor - stacionární stavy, jejich časový vývoj - časový vývoj pravděpodobností a středních hodnot ve stacionárním stavu - časový vývoj obecného stavu vyjádřeného v bázi stacionárních stavů - hustota toku pravděpodobnosti 8. Jednorozměrné problémy - řešení Schrödingerovy rovnice pro pravoúhlé potenciálové bariéry - diskrétní a spojité spektrum energií v jámě - odraz od bariéry, jámy a schodu - tunelování - příklady (hrot v elektronovém mikroskopu, alfa-rozpad, Josephsonův jev) 9. Harmonický oscilátor - zavedení kreačního a anihilačního operátoru, jejich komutátor - generování nových vlastních stavů hamiltoniánu - omezení energie zdola, spektrum možných hodnot energie - aplikace: fotony, fonony, Planckův vyzařovací zákon 10. Kvantování momentu hybnosti - vlastnosti trojrozměrných rotací, komutační relace pro složky momentu hybnosti - výběr vhodného systému komutujících veličin - žebříčkové operátory, tvoření nových vlastních stavů - celočíselný a poločíselný moment hybnosti, spinový stupeň volnosti - dalekosáhlé důsledky: rotační spektra molekul, stavy elektronů v atomu, výběrová pravidla pro přechod mezi stavy 11. Atom vodíku - přechod do těžišťové soustavy a ke sférickým souřadnicím - rozpad problému na úhlovou a radiální část - úhlová část - převedení na moment hybnosti - řešení radiální části, vlastní hodnoty energie, degenerace hladin 12. Přibližné metody - stacionární poruchová teorie, opravy k energii a koeficienty nových stacionárních stavů - degenerovaný případ, sekulární rovnice - časově proměnné poruchy, pravděpodobnost přechodu, Fermiho zlaté pravidlo - variační metoda a její aplikace v chemii 13. Identické částice - změna stavu při záměně částic - bosony a fermiony - fermiony - Slaterův determinant, Pauliho pincip, Fermiho energie - bosony - bunching, Cooperovy páry 14. Modernejší partie - provázanost (entanglement), Bellovy a GHZ stavy - popis podsystému pomocí matice hustoty - měření a kolaps stavu - Bellovy nerovnosti - zmínka o kvantové kryptografii, teleportaci, klonování a kvantových počítačích.
Literature
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
Assessment methods (in Czech)
Přednáška, cvičení
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2003
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
prof. RNDr. Michal Lenc, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
Basic course in nonrelativistic quantum mechanics. The probability amplitude and wavefuction. Formalism of quantum mechanics: mathematical tools, postulates, Schrödinger equation. One-dimensional problems - potential steps and barriers, tunneling. Quantization of a harmonic oscillator, angular momentum and of the hydrogen atom. Spin 1/2, Pauli matrices. Systems of identical particles. Approximative methods - time independent and dependent perturbation theory, Fermi golden rule, variational method. Density matrix, entangled states, Bell inequalities, Greenberger-Horne-Zeilinger states. Note on quantum cryptography, teleportation, cloning, and quantum computers.
Syllabus (in Czech)
  • 1. Motivace pro kvantovou mechaniku - neobvyklé chování kvantových objektů - úspěšnost kvantové fyziky při vysvětlení jevů týkajících se malých objektů - nezbytnost kvantové mechaniky pro pochopení i těch nejzákladnějších vlastností hmoty - aplikace v technologiích (počítače, mobilní telefony, nové materiály atd.) - chemická vazba - nelze porozumět bez kvantové mechaniky, podobně procesy v živé přírodě 2. Analogie geometrická vs. vlnová optika -- klasická vs. kvantová mechanika - trajektorie světelného paprsku daná Fermatovým principem - šíření světla po všech možných trajektoriích podle Huygensova-Fresnelova principu - trajektorie hmotného bodu daná Hamiltonovým principem - šíření hmotného po všech možných trajektoriích ve shodě s Feynmanovou formulací kvantové mechaniky 3. Pojem amplitudy pravděpodobnosti a vlnové funkce - událost a její amplituda pravděpodobnosti - princip superpozice pro amplitudy pravděpodobnosti, příklady - skládání pravděpodobností v klasické a kvantové mechanice - vlnová funkce - amplituda nalezení částice v daném místě prostoru - normování vlnové funkce 4. Kvantové stavy a operátory - Hilbertův prostor - fyzikální význam skalárního součinu - fyzikální veličiny a hermitovské operátory - možné výsledky měření fyzikální veličiny, spektrum operátoru - ortogonalita vlastních stavů, její fyzikální význam - rozklad jednotkového operátoru - střední hodnota operátoru 5. Souřadnicová reprezentace - stavy částice na přímce, vlnová funkce - operátor souřadnice a jeho vlastní stavy, Diracova delta funkce - operátor hybnosti jako generátor translace, vlastní stavy - komutační relace pro operátor souřadnice a hybnosti - přechod od souřadnicové k impulzové reprezentaci a zpět 6. Obecné relace neurčitosti - odvození relací neurčitosti v obecném tvaru - příklady: operátory souřadnice a hybnosti, složky momentu hybnosti - vlnová klubka, vlastní stavy momentu hybnosti 7. Schrödingerova rovnice - linearita časového vývoje, rovnice prvního řádu - Hamiltonův operátor - stacionární stavy, jejich časový vývoj - časový vývoj pravděpodobností a středních hodnot ve stacionárním stavu - časový vývoj obecného stavu vyjádřeného v bázi stacionárních stavů - hustota toku pravděpodobnosti 8. Jednorozměrné problémy - řešení Schrödingerovy rovnice pro pravoúhlé potenciálové bariéry - diskrétní a spojité spektrum energií v jámě - odraz od bariéry, jámy a schodu - tunelování - příklady (hrot v elektronovém mikroskopu, alfa-rozpad, Josephsonův jev) 9. Harmonický oscilátor - zavedení kreačního a anihilačního operátoru, jejich komutátor - generování nových vlastních stavů hamiltoniánu - omezení energie zdola, spektrum možných hodnot energie - aplikace: fotony, fonony, Planckův vyzařovací zákon 10. Kvantování momentu hybnosti - vlastnosti trojrozměrných rotací, komutační relace pro složky momentu hybnosti - výběr vhodného systému komutujících veličin - žebříčkové operátory, tvoření nových vlastních stavů - celočíselný a poločíselný moment hybnosti, spinový stupeň volnosti - dalekosáhlé důsledky: rotační spektra molekul, stavy elektronů v atomu, výběrová pravidla pro přechod mezi stavy 11. Atom vodíku - přechod do těžišťové soustavy a ke sférickým souřadnicím - rozpad problému na úhlovou a radiální část - úhlová část - převedení na moment hybnosti - řešení radiální části, vlastní hodnoty energie, degenerace hladin 12. Přibližné metody - stacionární poruchová teorie, opravy k energii a koeficienty nových stacionárních stavů - degenerovaný případ, sekulární rovnice - časově proměnné poruchy, pravděpodobnost přechodu, Fermiho zlaté pravidlo - variační metoda a její aplikace v chemii 13. Identické částice - změna stavu při záměně částic - bosony a fermiony - fermiony - Slaterův determinant, Pauliho pincip, Fermiho energie - bosony - bunching, Cooperovy páry 14. Modernejší partie - provázanost (entanglement), Bellovy a GHZ stavy - popis podsystému pomocí matice hustoty - měření a kolaps stavu - Bellovy nerovnosti - zmínka o kvantové kryptografii, teleportaci, klonování a kvantových počítačích.
Literature
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
Assessment methods (in Czech)
Přednáška, cvičení
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2002
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
prof. Mgr. Tomáš Tyc, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Celý, CSc.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: doc. RNDr. Jan Celý, CSc.
Prerequisites (in Czech)
( F4120 Theoretical mechanics && F4090 Electrodyn.and theory of rel. )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Basic course in nonrelativistic quantum mechanics. A short review of the origins of quantum theory. Solutions to Schrödinger's equation in one dimension. General fomalism of quantum mechanics: mathematical tools, postulates of quantum mechanics. Exactly soluble bound state problems: harmonic oscillator, angular momentum, spherically symetrical potencials, the hydrogen atom. Electron spin. Systems of identical particles. Time-independent aproximate methods: perturbation theory, variational methods. Time-dependent perturbation theory: transition rates and Fermi golden rule.
Literature
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
Assessment methods (in Czech)
Přednáška, cvičení
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Foundations of Quantum Mechanics

Faculty of Science
Autumn 2001
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
prof. Mgr. Tomáš Tyc, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Celý, CSc.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: doc. RNDr. Jan Celý, CSc.
Prerequisites (in Czech)
( F4120 Theoretical mechanics && F4090 Electrodyn.and theory of rel. )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Basic course in nonrelativistic quantum mechanics. A short review of the origins of quantum theory. Solutions to Schrödinger's equation in one dimension. General fomalism of quantum mechanics: mathematical tools, postulates of quantum mechanics. Exactly soluble bound state problems: harmonic oscillator, angular momentum, spherically symetrical potencials, the hydrogen atom. Electron spin. Systems of identical particles. Time-independent aproximate methods: perturbation theory, variational methods. Time-dependent perturbation theory: transition rates and Fermi golden rule.
Literature
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2000
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Celý, CSc.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: doc. RNDr. Jan Celý, CSc.
Prerequisites (in Czech)
( F4120 Theoretical mechanics && F4090 Electrodyn.and theory of rel. )||( F3070 Electricity and magnetism && F4080 Optics and atomic physics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Stručný historický přehled období 1900-1927. Bornova interpretace. Schrödingerova rovnice(1D úlohy). Formalizmus kvantové mechaniky:(A)matematický aparát, (B)postuláty a některé jejich obecné důsledky. Evoluční operátor, Heisenbergova reprezentace. Harmonický oscilátor, algebraické řešení, soubor nezávislých oscilátorů. Moment hybnosti, řešení v souř. reprezentaci i algebraické. Pohyb v centrálním poli, atom H. Zeemanův jev. Spin elektronu, doplnění do nerelativistické teorie. Soubory stejných mikročástic, souřadnicová reprezentace stavu, reprezentace obsazovacích čísel. Aproximativní metody: (a)stacionární poruchový počet, korekce k degenerovaným stavům, (b)variační metody, (c)nestacionární poruchový počet, pravděpodobnosti přechodů. Semiklasická teorie interakce atomu s elektromagnetickým polem.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 1999
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Celý, CSc.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: doc. RNDr. Jan Celý, CSc.
Prerequisites (in Czech)
( F4120 Theoretical mechanics && F4090 )||( F3070 Electricity and magnetism && F4080 )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Syllabus (in Czech)
  • Stručný historický přehled období 1900-1927. Bornova interpretace. Schrödingerova rovnice(1D úlohy). Formalizmus kvantové mechaniky:(A)matematický aparát, (B)postuláty a některé jejich obecné důsledky. Evoluční operátor, Heisenbergova reprezentace. Harmonický oscilátor, algebraické řešení, soubor nezávislých oscilátorů. Moment hybnosti, řešení v souř. reprezentaci i algebraické. Pohyb v centrálním poli, atom H. Zeemanův jev. Spin elektronu, doplnění do nerelativistické teorie. Soubory stejných mikročástic, souřadnicová reprezentace stavu, reprezentace obsazovacích čísel. Aproximativní metody: (a)stacionární poruchový počet, korekce k degenerovaným stavům, (b)variační metody, (c)nestacionární poruchový počet, pravděpodobnosti přechodů. Semiklasická teorie interakce atomu s elektromagnetickým polem.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
General note: základní kurz M a F.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discretness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discretness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Introductory course in nonrelativistic quantum mechanics.
Main objectives can be summarized as follows: to master the basic mathematical tools used in quantum mechanics; to understand the concept of probability amplitude and wavefunction; to be able to solve Schroedinger equation in simple situations (potential wells, steps and barriers, harmonic oscillator, hydrogen atom); to be able to apply approximative methods (perturbation theory, variation method) in the simplest situations.
Syllabus
  • I. Introduction
  • 1. Concepts in the physics of microscopic phenomena: discretness, wave-particle dualism, uncertainty, complementarity, superposition.
  • 2. One-particle wave mechanics: de Broglie waves, Schroedinger equation, general properties of its solutions in the one-dimensional case, particle in a rectangular potential well, tunneling through a square potential barrier, mention of applications in the field of semiconductor nanostructures.
  • 3. Probability interpretation of the wave function and of its Fourier transform, mean values of functions of the position and the momentum, position-momentum uncertainty relation.
  • 4. Examples of systems of a finite dimension and a sketch of their quantum mechanical description (particle with a few discrete levels available, spin, polarization state of the electromagnetic radiation).
  • II. Formalism
  • 1. Abstract Hilbert space, state vectors and their representations, linear operators and their representations, hermitean operators and their properties.
  • 2. Postulates of the quantum mechanics concerning the description of the state of a system, dynamical variables, and measurement; uncertainty relations in the general case, complete sets of commuting operators.
  • 3. Evolution in time: Schroedinger equation in the general case, Heisenberg representation, connections with classical physics (Ehrenfest theorem, Classical limit of the Schroedinger equation), stationary case.
  • III. Applications
  • 1. The Harmonic oscillator: solution of the problem by the algebraic method involving the creation and annihilation operators, energy spectrum and wave functions, limit of large quantum numbers, mention of applications in the theory of black-body radiation and in the theory of the dynamics of the nuclei.
  • 2. Angular momentum in quantum mechanics: commutation relations for the components of the orbital angular momentum, extension to the components of the total angular momentum of an arbitrary system, determination of the eigenvalues of the magnitude of the angular momentum and of its selected component using the algebraic method, eigenfunctions of the orbital angular momentum, spin angular momentum, basics of the theory of the addition of angular momenta.
  • 3. Central field: simplification of the problem using the rotation symmetry of the hamiltonian, radial Schroedinger equation and a sketch of its solution, energy spectrum and eigenfunctions of the hydrogen-atom problem.
  • 4. Methods of approximation: stationary perturbation theory both for non-degenerate levels and for a degenerate level, time-dependent perturbation theory, perturbation calculation of inter-level transition probabilities, Fermi golden rule, mention of applications in the theory of optical response, variational method, mention of applications in quantum chemistry.
  • 5. Systems of identical particles: postulate concerning the symmetry/antisymmetry of the wavefunctions of a system of identical particles, bosons and fermions, relation between symmetry and spin, Pauli principle, wavefunctions of systems of noninteracting particles, mention of applications in the condensed matter theory (the ground state of the Bose-Einstein condensate, the Fermi sea).
Literature
  • ZETTILI, Nouredine. Quantum mechanics : concepts and applications. Chichester: John Wiley & Sons, 2001. xiv, 649. ISBN 0471489441. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xii, 504-9. ISBN 8020011765. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Quantum mechanics : non-relativistic theory. Translated by J. B. Sykes - J. S. Bell. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677. ISBN 0750635398. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • PIŠÚT, Ján, Ladislav GOMOLČÁK and Vladimír ČERNÝ. Úvod do kvantovej mechaniky [Pišút, 1983]. 2. vyd. Bratislava: Alfa, 1983. 551 s. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
Teaching methods
Lectures and class exercises, where solutions of typical problems are presented and discussed.
Assessment methods
The examination involves a written part (test consisting of ca 20 simple questions and/or problems, and solution of two or three more complicated problems) and an oral part. At least one half of the items of the test should be answered/solved for the student to complete the examination successfully. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~tomtyc/kvantovka.html
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.

F5030 Introduction to Quantum Mechanics

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Tomáš Tyc, Ph.D. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: prof. Mgr. Tomáš Tyc, Ph.D.
Prerequisites (in Czech)
( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
Basic course in nonrelativistic quantum mechanics. The probability amplitude and wavefuction. Formalism of quantum mechanics: mathematical tools, postulates, Schrödinger equation. One-dimensional problems - potential steps and barriers, tunneling. Quantization of a harmonic oscillator, angular momentum and of the hydrogen atom. Spin 1/2, Pauli matrices. Systems of identical particles. Approximative methods - time independent and dependent perturbation theory, Fermi golden rule, variational method. Density matrix, entangled states, Bell inequalities, Greenberger-Horne-Zeilinger states. Note on quantum cryptography, teleportation, cloning, and quantum computers.
Syllabus (in Czech)
  • 1. Motivace pro kvantovou mechaniku - neobvyklé chování kvantových objektů - úspěšnost kvantové fyziky při vysvětlení jevů týkajících se malých objektů - nezbytnost kvantové mechaniky pro pochopení i těch nejzákladnějších vlastností hmoty - aplikace v technologiích (počítače, mobilní telefony, nové materiály atd.) - chemická vazba - nelze porozumět bez kvantové mechaniky, podobně procesy v živé přírodě 2. Analogie geometrická vs. vlnová optika -- klasická vs. kvantová mechanika - trajektorie světelného paprsku daná Fermatovým principem - šíření světla po všech možných trajektoriích podle Huygensova-Fresnelova principu - trajektorie hmotného bodu daná Hamiltonovým principem - šíření hmotného po všech možných trajektoriích ve shodě s Feynmanovou formulací kvantové mechaniky 3. Pojem amplitudy pravděpodobnosti a vlnové funkce - událost a její amplituda pravděpodobnosti - princip superpozice pro amplitudy pravděpodobnosti, příklady - skládání pravděpodobností v klasické a kvantové mechanice - vlnová funkce - amplituda nalezení částice v daném místě prostoru - normování vlnové funkce 4. Kvantové stavy a operátory - Hilbertův prostor - fyzikální význam skalárního součinu - fyzikální veličiny a hermitovské operátory - možné výsledky měření fyzikální veličiny, spektrum operátoru - ortogonalita vlastních stavů, její fyzikální význam - rozklad jednotkového operátoru - střední hodnota operátoru 5. Souřadnicová reprezentace - stavy částice na přímce, vlnová funkce - operátor souřadnice a jeho vlastní stavy, Diracova delta funkce - operátor hybnosti jako generátor translace, vlastní stavy - komutační relace pro operátor souřadnice a hybnosti - přechod od souřadnicové k impulzové reprezentaci a zpět 6. Obecné relace neurčitosti - odvození relací neurčitosti v obecném tvaru - příklady: operátory souřadnice a hybnosti, složky momentu hybnosti - vlnová klubka, vlastní stavy momentu hybnosti 7. Schrödingerova rovnice - linearita časového vývoje, rovnice prvního řádu - Hamiltonův operátor - stacionární stavy, jejich časový vývoj - časový vývoj pravděpodobností a středních hodnot ve stacionárním stavu - časový vývoj obecného stavu vyjádřeného v bázi stacionárních stavů - hustota toku pravděpodobnosti 8. Jednorozměrné problémy - řešení Schrödingerovy rovnice pro pravoúhlé potenciálové bariéry - diskrétní a spojité spektrum energií v jámě - odraz od bariéry, jámy a schodu - tunelování - příklady (hrot v elektronovém mikroskopu, alfa-rozpad, Josephsonův jev) 9. Harmonický oscilátor - zavedení kreačního a anihilačního operátoru, jejich komutátor - generování nových vlastních stavů hamiltoniánu - omezení energie zdola, spektrum možných hodnot energie - aplikace: fotony, fonony, Planckův vyzařovací zákon 10. Kvantování momentu hybnosti - vlastnosti trojrozměrných rotací, komutační relace pro složky momentu hybnosti - výběr vhodného systému komutujících veličin - žebříčkové operátory, tvoření nových vlastních stavů - celočíselný a poločíselný moment hybnosti, spinový stupeň volnosti - dalekosáhlé důsledky: rotační spektra molekul, stavy elektronů v atomu, výběrová pravidla pro přechod mezi stavy 11. Atom vodíku - přechod do těžišťové soustavy a ke sférickým souřadnicím - rozpad problému na úhlovou a radiální část - úhlová část - převedení na moment hybnosti - řešení radiální části, vlastní hodnoty energie, degenerace hladin 12. Přibližné metody - stacionární poruchová teorie, opravy k energii a koeficienty nových stacionárních stavů - degenerovaný případ, sekulární rovnice - časově proměnné poruchy, pravděpodobnost přechodu, Fermiho zlaté pravidlo - variační metoda a její aplikace v chemii 13. Identické částice - změna stavu při záměně částic - bosony a fermiony - fermiony - Slaterův determinant, Pauliho pincip, Fermiho energie - bosony - bunching, Cooperovy páry 14. Modernejší partie - provázanost (entanglement), Bellovy a GHZ stavy - popis podsystému pomocí matice hustoty - měření a kolaps stavu - Bellovy nerovnosti - zmínka o kvantové kryptografii, teleportaci, klonování a kvantových počítačích.
Literature
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP, 1986. 176 s. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. II, Aplikace. 1. vyd. Brno: Rektorát UJEP, 1983. 161 s. info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company, 1993. vii, 782 s. ISBN 0-201-54715-5. info
  • MATTHEWS, Paul T. Základy kvantové mechaniky [Matthews, 1976]. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1976. 256 s. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall, 1995. 9, 394 s. ISBN 0-13-124405-1. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Úvod do teoretickej fyziky. 2, Kvantová mechanika. 1. vyd. Bratislava: Alfa, 1982. 357 s. info
  • MARX, György. Úvod do kvantové mechaniky. 1. vyd. Praha: Státní nakladatelství technické literatury, 1965. 294 s. info
  • BLOCHINCEV, D. I. Základy kvantové mechaniky [Blochincev, 1956]. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1956. 545 s. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika [Davydov, 1978] : Kvantovaja mechanika (Orig.). 1. vyd. Praha: Státní pedagogické nakladatelství, 1978. 685 s. info
Assessment methods (in Czech)
Přednáška, cvičení
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.
  • Enrolment Statistics (recent)