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 6/1014
F5030/02: Wed 12:00–13:50 Fs1 6/1017
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. xiv, 649. ISBN 0471489441. 2001. info
  • FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia. xii, 504-9. ISBN 8020011765. 2004. info
  • GRIFFITHS, David Jeffrey. Introduction to quantum mechanics. Englewood Cliffs: Prentice Hall. 9, 394 s. ISBN 0-13-124405-1. 1995. info
  • MARX, György. Úvod do kvantové mechaniky. Translated by Luděk Bednář - Zdeněk Urbánek. Vyd. 1. Praha: Státní nakladatelství technické literatury. 294 s. 1965. URL 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. xv, 677. ISBN 0750635398. 1977. info
  • BLOCHINCEV, Dimitrij Ivanovič. Základy kvantové mechaniky. Translated by Jan Cejpek. 1. vyd. Praha: Nakladatelství Československé akademie věd. 545 s. 1956. URL info
  • MATTHEWS, Paul T. Základy kvantové mechaniky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury. 256 s. 1976. URL info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. I, Principy [Celý, 1986]. 1. vyd. Brno: Rektorát UJEP. 176 s. 1986. info
  • CELÝ, Jan. Základy kvantové mechaniky pro chemiky. Vyd. 1. Brno: Rektorát UJEP. 161 s. 1983. info
  • DAVYDOV, Aleksandr Sergejevič. Kvantová mechanika. Vyd. 1. Praha: Státní pedagogické nakladatelství. 685 s. 1978. URL info
  • LIBOFF, Richard L. Introductory quantum mechanics. 2nd ed. Reading: Addison-Wesley Publishing Company. vii, 782 s. ISBN 0-201-54715-5. 1993. 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.
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, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2009, recent)
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