Relationship between the Wigner function and the probability density function in quantum phase space representation

Abstract

This paper discusses the relationship between the Wigner function, along with other related quasiprobability distribution functions, and the probability density distribution function constructed from the wave function of the Schr\odinger equation in quantum phase space, as formulated by Torres-Vega and Frederick (TF). At the same time, a general approach in solving the wave function of the Schr\odinger equation of TF quantum phase space theory is proposed. The relationship of the wave functions between the TF quantum phase space representation and the coordinate or momentum representation is thus revealed.