UFTF003 Quantum Mechanics II

Faculty of Philosophy and Science in Opava
Winter 2022
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Mikuláš Gintner, Ph.D. (lecturer)
RNDr. Josef Juráň, Ph.D. (lecturer)
RNDr. Filip Blaschke, Ph.D. (seminar tutor)
RNDr. Mikuláš Gintner, Ph.D. (seminar tutor)
RNDr. Josef Juráň, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Josef Juráň, Ph.D.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Prerequisites
Knowledge of bachelor course of quantum mechanics.
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
The course is a continuation of the course of Quantum Mechanics I. The new course is extended and supplemented. In the beginning approximate methods of quantum mechanics are shown, namely, generalized perturbation theory and variational methods. In the following, the theory of multi-particle systems, interaction of radiation with matter, and quantum scattering theory. The course is closed by relativistic quantum mechanics.
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
  • Mathematical basis of Quantum Mechanics: Axioms of Quantum Mechanics
    theory of representations (coordinate, momentum, energy), unitary
    transformations, pictures of Quantum Mechanics (Schrödinger, Heisenberg,
    Dirac) pure and mixed states, density operator.
    Approximated methods of quantum theory: Generalized perturbation theory, Stark effect;
    variational method.
    Angular momentum II: Operator of generalized angular momentum addition of
    angular momenta, Clebsch-Gordon coefficients spin-orbit and spin-spin
    interactions fine structure of hydrogen, Zeeman effect.
    Multi-particle systems: Wavefunction and its physical meaning spin variables
    systems of identical particles exchange operator symmetric and
    antisymmetric wavefunctions, Pauli exclusion principle bosons and fermions.
    Helium: Calculation of energy levels by perturbative and variational methods
    two-electron spin functions excited states orthohelium and parahelium.
    Elementary theory of molecules: Adiabatic approximation hydrogen molecule
    vibrational, rotational and electron states of two-atom molecules.
    Interaction of quantum system with electromagnetic radiation: Nonstationary perturbation method, Fermi Golden Rule; longwave
    approximation, selection rules for emission and absorption; Einstein coefficients; quantum multipole expansion.
    Quantum scattering theory: Born approximation Partial wave analysis S-matrix
    resonances.
    Relativistic wave equations: Klein-Gordon equation, Dirac equation, continuity
    equation, interaction with electromagnetic field, non-relativistic limit,
    spin and intrinsic magnetic moment of Dirac particle.
Literature
    required literature
  • Skála L. Úvod do kvantové mechaniky. Praha, 2005. ISBN 80-200-1316-4. info
    recommended literature
  • Weinberg S. Lectures on Quantum Mechanics. Cambridge, 2015. ISBN 978-1-107-11166-0. info
  • Klíma J., Šimurda M. Sbírka problémů z kvantové teorie. Praha, 2006. info
  • Shankar R. Principles of Quantum Mechanics. New York, 1994. info
  • Pišút J., Černý V., Prešnajder P. Zbierka úloh z kvantovej mechaniky. Bratislava/Praha, 1985. info
  • Pišút J., Gomolčák L., Černý V. Úvod do kvantovej mechaniky. Bratislava/Praha, 1983. info
  • Davydov A.S. Kvantová mechanika. Praha, 1978. info
    not specified
  • Formánek J. Úvod do kvantové teorie. Praha, 2004. ISBN 80-200-1176-5. info
Teaching methods
One-to-One tutorial
Monological (reading, lecture, briefing)
Internship
Students' self-study
Assessment methods
Test
Written exam
Credit
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
* attendance in lectures and tutorials, active participation
and/or self-study of selected parts of recommended literature (homeworks)
* a few short written tests during semester (success rate 50 %)
* written and oral exam
The course is also listed under the following terms Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2023.
  • Enrolment Statistics (Winter 2022, recent)
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