This lecture introduces the fundamental concepts of group theory and their representations. The accent is on the concrete applications of the mathematical concepts to practical quantum mechanical problems of solid state physics and other fields of physics rather than on their mathematical proof.
Learning objective
The aim of this lecture is to give a fundamental knowledge on the application of symmetry in atoms, molecules and solids. The lecture is intended for students at the master and Phd. level in Physics that would like to have a practical and comprehensive view of the role of symmetry in physics. Students in their third year of Bachelor will be perfectly able to follow the lecture and can use it for their future master curriculuum. Students from other Departement are welcome, but they should have a solid background in mathematics and physics, although the lecture is quite self-contained.
Content
1. Groups, Classes, Representation theory, Characters of a representation and theorems involving them.
2. The symmetry group of the Schrödinger equation, Invariant subspaces, Atomic orbitals, Molecular vibrations, Cristal field splitting, Compatibility relations, Band structure of crystals.
3. SU(2) and spin, The double group, The Kronecker Product, The Clebsch-Gordan coefficients, Clebsch-Gordan coeffients for point groups,The Wigner-Eckart theorem and its applications to optical transitions.
Lecture notes
The copy of the blackboard is made available online.
Literature
This lecture is essentially a practical application of the concepts discussed in:
- L.D. Landau, E.M. Lifshitz, Lehrbuch der Theor. Pyhsik, Band III, "Quantenmechanik", Akademie-Verlag Berlin, 1979, Kap. XII - Ibidem, Band V, "Statistische Physik", Teil 1, Akademie-Verlag 1987, Kap. XIII and XIV.
Performance assessment
Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course