Group Theory and Symmetries in Quantum Mechanics (S17)

Group theory and symmetries in quantum mechanics

Lecturer:
Dr. Andrey Moskalenko

The course gives a general introduction to the aspects of the group theory in view of applications in quantum mechanics. The underlying formalism will be discussed for both discrete and continuous groups. Relation to general symmetries of quantum-mechanical systems will be illuminated. We will show how these symmetries result in certain selection rules for the transitions between states in atomic, molecular, and solid-state systems. Further applications of group theory that will be considered include:
i) analysis of the electronic and vibrational spectra of atomic and molecular systems as well as defect states in solids,
ii) band structures of crystalline solids,
iii) mesons and baryons as combinations of quarks and antiquarks.

Required: linear algebra, quantum mechanics (can be completed in parallel)
Recommended: solid state physics

Literature:
1) J. P. Elliott and P. G. Dawber, Symmetry in Physics (Macmillan, 1979).
2) M.S. Dresselhaus, G. Dresselhaus, and A. Jorio, Group Theory: Application to the Physics of Condensed Matter (Springer, 2008).
3) M. Tinkham, Group Theory and Quantum Mechanics (Dover, 1964, 1992, 2003).
4) W.-K. Tung, Group Theory in Physics (World Scientific, 1985).
5) W. Greiner and B. Müller, Quantum Mechanics: Symmetries (Springer, 1994).

Termine

  • Vorlesung: Raum P603
    Di 13:30-15:00 Uhr
    Fr 10:00-11:30 Uhr
  • Beginn der Vorlesung: 2.05.2017 (2. Vorlesungswoche!)
  • Übungen
  • Mi 10:00-11:30 Uhr, L602 - Alexander Pearce
    Mi 11:45-13:15 Uhr, PZ0901 - Thiago Lucena
    Do 11:45-13:15 Uhr, M1001 - Vladislav Shkolnikov

    Exercise sheets

    Sheet 1
    Sheet 2
    Sheet 3
    Sheet 4
    Sheet 5
    Sheet 6
    Sheet 7
    Sheet 8
    Sheet 9
    Sheet 10
    Sheet 11

  • Ende der Lehrveranstaltungen: 28.08.2017
  • Prüfungen
  • Mündliche Prüfung: Dienstag, 8.08.2017

    Schriftliche Prüfung: Mittwoch, 2.08.2017, 11:00-14:00 (!!!), R 711
    Erlaubte Hilfsmittel:
    Nur Schreibmaterial und ein beidseitig beschriebenes A4 Blatt (keine Taschenrechner, keine Handys/Smartphones usw.)