Quasi-probability distributions for arbitrary spin-j particles

Abstract

Quasi-probability distribution functions fjWW, fjMM for quantum spin-j systems are derived based on the Wigner-Weyl, Margenau-Hill approaches. A probability distribution fjsph which is nonzero only on the surface of the sphere of radius √j(j+1) is obtained by expressing the characteristic function in terms of the spherical moments. It is shown that the Wigner-Weyl distribution function turns out to be a distribution over the sphere in the classical limit.