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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)

doc. Mgr. Dominik Munzar, Dr. (lecturer)
doc. Franz Hinterleitner, Ph.D. (seminar tutor)

Supervisor

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 (v češtině)

( F4120 Theoretical mechanics )
Absolvování základního kurzu fyziky.

Course Enrollment Limitations

The course is only offered to the students of the study fields the course is directly associated with.

Fields of study 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 s. ISBN 0-471-48944-1. info
FORMÁNEK, Jiří. Úvod do kvantové teorie. Vyd. 2., upr. a rozš. Praha: Academia, 2004. xx, 502, 1. ISBN 80-200-1176-5. 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. Edited by J. S. Bell, Translated by J. B. Sykes. 3rd ed., rev. and enl. Amsterdam: Butterworth-Heinemann, 1977. xv, 677 s. ISBN 0-7506-3539-8. 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.

Follow-Up Courses

Further Comments