Introduction to the Formalism of the Space of Spin States. The Hamiltonian Operator

Abstract

This chapter provides a toolbox to analyze the shape and the intensity of EPR spectra and introduces the vector space associated with angular momentum and the operations that can be performed on its vectors. The signification and use of the spin Hamiltonian are discussed. This formalism is then used to determine the possible spin states and energy levels of a paramagnetic center with an anisotropic magnetic moment in an external magnetic field. The selection rules giving the allowed transitions are justified. Next, the principle of perturbation theory is presented in a simple way, and this theory is used to determine the allowed transitions when a paramagnetic center is subjected to hyperfine interactions in the isotropic regime.