Electron Spin and General Angular Momenta

Abstract

The historical background of the discovery of the electron spin is provided. The Stern-Gerlach and Einstein-de Haas experiments are discussed. The operators for a single electron spin are defined, along with the formulation in terms of the 2x2 Pauli matrices. The discussion then moves on to the definition of the spin for many-electron systems and explains how the famous Hund rule (or Hund’s first rule) arises from considering the energy of an open-shell spin singlet vs. triplet state. Next, the generalized angular momentum, ladder operators, and spherical vector operators are defined, and the rules for the addition of angular momenta are derived. The chapter concludes with a discussion of the total spin, orbital, and total angular momentum for open-shell atoms, term symbols, and Hund’s second and third rule.