On the calculation of spin densities

Abstract

Methods are presented for calculating the expectation value of the spin density for the state resulting from spin-projection of an anti-symmetrized spin-orbital product. It is found that the spin densities for projected and unprojected states differ in the coefficients of the various spatial terms, and that these coefficients can be determined from the properties of the spin algebra. It is shown how the coefficients needed for the spin density are related to those previously derived by other workers for spin-free operators. Illustrative cases of the formalism are examined in detail to show how the calculated z component of the spin density depends upon the total spin as well as upon its z component.