Use of Group Theory in Semiconductors

This set of lectures is intended as an introduction to the use of group theory in the study of solids in general, with emphasis on Semiconductors. Chapters from Yu and Cardona's book (Semiconductor Physics) and chapter 12 of Landau and Lifshitz’s book (Quantum Mechanics) will form the basis. Only those proofs will be given which are short and subtle and provide some insight into the use of symmetry.  Outline of topics to be covered is given below. 

1) Basics: definitions (group, multiplication table, conjugate classes, basis sets) important  concepts, useful theorems 
2) Irreducible representations, how to find them, character tables, orthogonality relations
3) Using group theory to obtain degeneracy and splitting of levels under a perturbation
4) Selection rules
5) Example 1: empty lattice band structure and plane wave combinations for irreducible representations 
6) Example 2: symmetry of vibrational modes in a molecule
7) Example 3: crystal field splitting of impurity levels