The Phase Space Distributions and the Correspondence Principle

Abstract

An attempt is made to obtain a correspondence between the classical mechanics and the Wigner-type quantum mechanics by analyzing a particular solution to the quasiprobability operator equation. We have applied this solution to yield ground state energies in the case of an equilibrium distribution which is a limit ofa quantum distribution with the time coordinate tending to infinity. The presence of an arbitrary parameter in our solution is now explicitly fixed by the ground state energy that must be reflected in the solution to the generalized Fokker-Planck equation. An appropriate choice ofboundary conditions dictated by the quantum constraints now guarantee a unique solution to the equation of motion.