Group Theory in Stationary Perturbation Theory Calculations

This chapter focuses on the usefulness of group theory in the stationary perturbation theory. In Sect. 8.1, we revisit Rayleigh-Schrödinger perturbation theory. The concept of the subduced representation and its reduction are relevant for degenerate perturbation theory, which we discuss in Sections 8.2 and 8.3. In Sect. 8.4, we explore an application crucial for solid-state physics: the splitting of atomic spectra in crystal fields. Finally, in Sect. 8.5, we investigate how to analyze matrix elements in perturbation theory with group theoretical means.