Chapter 9 - The electron spin

Abstract

The theory of one-electron and two-electron spin according to Pauli is formally developed, even in matrix form, and then extended to the many-electron case, including the Dirac’s formulation of the many-spin problem. It is seen that the latter is connected to the permutational symmetry of the many-electron wavefunctions treated in the chapter on group theory. Since the formalism derived is in one-to-one correspondence with that of the spin-orbitals needed for the correct description of the many-electron wavefunctions in the Slater method, it is possible to treat explicitly spin states alone. Lastly, to construct states of definite spin, we introduce the matrix method based on diagonalization of the matrix representatives of spin operators, the Kotani’ synthetic method based on the branching diagram, and the analytic Löwdin’ spin projector method based on the annihilation of unwanted spin components. What said for the electron spin is valid for 1H and 13C nucler spins.