Probabilistic aspects of Wigner function
  The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is applied as well to seek indications of specific quantum properties of quantum systems leading to impossibility of the classical approximation construction. Most of all, as such an indication the existence of negative values in Wigner function for specific states of the quantum system being studied is used. The existence of such values itself prejudices the probabilistic interpretation of the Wigner function, though for an arbitrary observable depending jointly on the coordinate and the momentum of the quantum system just the Wigner function gives an effective instrument to calculate the average value and the other statistical characteristics.   In this paper probabilistic interpretation of the Wigner function based on coordination of theoretical-probabilistic definition of the probability density, with restrictions to a physically small domain of phase space due to the uncertainty principle, is proposed. 
Constantin V. Usenko