Group Theory and Symmetries in Quantum Mechanics (S15)

Group theory and symmetries in quantum mechanics

Lecturers:
Dr. A. Kormanyos
Dr. A. Moskalenko
Prof. G. Burkard

Prerequisites (Voraussetzung): linear algebra (Lineare Algebra I), quantum mechanics (IK4)
Recommended (empfohlen): solid state physics (Festkörperphysik)

The course gives an introduction to the main general aspects of the group theory in view of applications in quantum mechanics. General symmetries, which are relevant for quantum mechanical systems, the theory of angular momentum and many-particle states will be discussed in this context. Applications of the group theory for the analysis of the electronic, vibronic and rotational spectra of atomic and molecular systems will be presented. The group-theoretical techniques will be also used to discuss the band structures of crystalline solids and as well as for construction of effective Hamiltonians at high symmetry points in the reciprocal space on the basis of symmetry considerations. We will show how symmetry implications result in certain selection rules for the transitions between states in atomic, molecular, and solid state systems.

Literature:
1) W.-K. Tung, Group Theory in Physics (World Scientific, 1985).
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) J. P. Elliott and P. G. Dawber, Symmetry in Physics (Macmillan, 1979).
5) W. Greiner and B. Müller, Quantum Mechanics: Symmetries (Springer, 1994).

Termine

  • Vorlesung:
    Mo 15:15-16:45 Uhr, P 603
    Do 13.30-15.00 Uhr, P 603
  • Beginn der Vorlesung: 13.04.2015
  • Übungen
  • Di 17.00-18:30 Uhr P1012 Heng Wang

    Exercise sheets

    Sheet 1
    Sheet 2
    Sheet 3
    Sheet 4
    Sheet 5
    Sheet 6
    Sheet 7
    Sheet 8
    Sheet 9
    Sheet 10
    Sheet 11
    Sheet 12
    Sheet 13

  • Ende der Lehrveranstaltungen: 17.07.2015
  • Prüfungen
  • Mündliche Prüfung: Dienstag, 28.07.15

    Schriftliche Prüfung: Mittwoch, 29.07.15 , 10:00-13:00, P712
    Erlaubte Hilfsmittel:
    Nur Schreibmaterial und ein beidseitig beschriebenes A4 Blatt (keine Taschenrechner, keine Handys/Smartphones usw.)