FYBAF0004 Introduction to Quantum Mechanics

Institute of physics in Opava
winter 2021
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Josef Juráň, Ph.D. (lecturer)
Guaranteed by
RNDr. Josef Juráň, Ph.D.
Institute of physics in Opava
Prerequisites (in Czech)
(FAKULTA(FU) && TYP_STUDIA(B))
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
Course objectives
After historical overview the basic concept of quantum theory is introduced. Mathematical apparatus is established and axioms of quantum mechanics are set. Schrödinger equation is solved for basic physical problems including hydrogen atom.
Learning outcomes
Upon successful graduation from the subject, a student will understand concept of quantum theory; will be able to formulate and solve elementary problems in quantum mechanics; to calculate and analyze energy spectrum of hydrogen atom.
Syllabus
  • History of quantum physics. Young experiment, black-body radiation, Thomson model, photoelectric effect, Rutherford experiment, Bohr model, Franck-Hertz experiment, Compton scattering, de Broglie wave.
  • Basic concept and principles of quantum physics. Wave function and its probabilistic interpretation, superposition principle. Hilbert space. Expectation value of position and momentum of particle, momentum operator.
  • Mathematical operator theory. Eigenfunctions and their eigenvalues. Types of spectra. Commutators. Hermitian operators. Operators of basic physical quantities.
  • Measurement, wave function collapse.
  • Uncertainty principle, Heisenberg's uncertainty principle.
  • Time evolution of wave function. Schrödinger equation. Stationary state. Time-dependence of expectation values of physical quantities. Ehrenfest theorem.
  • Continuity equation in quantum mechanics, probability current.
  • Solution of Schrödinger equation. Free particle, potential well and three-dimensional box, linear harmonic oscillator, potential barrier, quantum tunnelling.
  • Angular momentum operator, its eigenvalues and eigenfunctions.
  • Motion in central potential field. Hydrogen atom and its spectrum. Hydrogen atom in magnetic field, normal Zeeman effect.
  • Spin. Stern-Gerlach experiment, spin operator, spinors.
  • Interpretation of quantum mechanics.
Literature
    required literature
  • Skála L. Úvod do kvantové mechaniky. Praha, 2005. ISBN 80-200-1316-4. info
    recommended literature
  • J. Pišút, L. Gomolčák, V. Černý. Úvod do kvantovej mechaniky. Bratislava/Praha, ALFA/SNTL, 1983.
  • J. Pišút, V. Černý, P. Prešnajder. Zbierka úloh z kvantovej mechaniky. Bratislava/Praha, ALFA/SNTL, 1985.
  • Klíma J., Šimurda M. Sbírka problémů z kvantové teorie. Academia, 2006.
    not specified
  • Griffiths D. J., Schroeter D. F. Introduction to Quantum Mechanics. Cambridge, 2018.
  • Weinberg S. Lectures on Quantum Mechanics. Cambridge, 2015
Teaching methods
Monological (lecture, briefing)
Tutorial
Students' self-study
One-to-One tutorial
Assessment methods
homework
random test
written test
oral and written exam
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms winter 2020, winter 2022, winter 2023, winter 2024.
  • Enrolment Statistics (winter 2021, recent)
  • Permalink: https://is.slu.cz/course/fu/winter2021/FYBAF0004