Splitting of Atomic Orbitals in a Crystal Potential

Abstract

This is the first of several chapters aimed at presenting some general applications of group theory while further developing theoretical concepts and amplifying on those given in the first four chapters. The first application of group theory is made to the splitting of atomic energy levels when the atom is placed in a crystal potential, because of the relative simplicity of this application and because it provides a good example of going from higher to lower symmetry, a procedure used very frequently in applications of group theory to solid state physics. In this chapter we also consider irreducible representations of the full rotation group.