Group Theory and Symmetries in Quantum Mechanics (S16)

Group theory and symmetries in quantum mechanics

Dr. A. Kormányos
Prof. G. Burkard

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

The course gives a general introduction to the aspects of Group Theory that can help to solve problems in quantum mechanics.
The basic mathematical ingredients will be discussed for both discrete and continuous groups. The relation to general symmetries,
which are relevant for quantum mechanical systems, will be discussed in this context. We will show how symmetries of a system
result in certain selection rules for the transitions between states in atomic, molecular, and solid state physics.
Further applications of group theory that we will consider include:
i) analysis of the electronic and vibrational spectra of atomic and molecular systems
ii) group-theoretical techniques will be also used to discuss the band structures of crystalline solids
iii) we will give examples of how group theoretical considerations can help to understand certain properties
of quarks, barions and mesons, i.e., the basic building blocks of matter.

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).