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PřF:F5030 Intro. to Quantum Mechananics - Course Information

## 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)

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:

**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

- ZETTILI, Nouredine.
**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

- Enrolment Statistics (recent)

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