UFTF003 Quantum Mechanics II

Faculty of Philosophy and Science in Opava
Winter 2015
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)
doc. RNDr. Filip Blaschke, Ph.D. (seminar tutor)
RNDr. Mikuláš Gintner, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Josef Juráň, Ph.D.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Prerequisites (in Czech)
Znalost základního kurzu kvantové mechaniky na úrovni bakalářského stupně studia.
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, quantum scattering theory, interaction of radiation with matter, and relativistic quantum mechanics are discussed. The course is closed by part which sum up a significance of symmetries and conservation laws in quantum mechanics.
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.
Quantum scattering theory: Partial wave analysis Born approximation S-matrix
resonances.
Interaction of quantum system with electromagnetic radiation: Longwave
approximation selection rules for emission and absorption, quantum multipole
expansion.
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.
Utilization of groups in Quantum Mechanics: Operation of symmetry symmetries
and conservation laws.
Literature
    required literature
  • Skála L. Úvod do kvantové mechaniky. Praha, 2005. ISBN 80-200-1316-4. info
    recommended literature
  • 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 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023.
  • Enrolment Statistics (Winter 2015, recent)
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