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The Wigner picture of quantum mechanics constitutes a phase space formulation of the quantum theory. Both states and observables are represented by functions of the phase space coordinates. The Weyl transform attributes to any given operator of the wave mechanics a phase space counterpart which is a c-number. Furthermore, the Wigner function is both the phase space counterpart of the density matrix and the quantum counterpart of the classical distribution function. Basic notions of the classical statistical mechanics are retained in this picture. In particular the usual quantities of interest in operator quantum mechanics, i.e. mean values and probabilities, are evaluated in the phase space by rules resembling the formulae of the classical statistics. It is for these reasons that the Wigner function is often apprehended as a quasi-distribution.
The phase space formulation of quantum mechanics has been established historically on top of the operator mechanics. However, the Wigner theory can be derived as an equivalent autonomous alternative of the operator mechanics. Important questions about what outlines classical from quantum behavior in the phase space and how to determine if a given function of the phase space coordinates is a possible quantum or classical state have been addressed by the inverse approach which provides an independent formulation of the Wigner theory.
Actually the Wigner formalism attracts growing interest for theoretical and numerical development and applications in many different fields in non-equilibrium statistical physics, nanoelectronics, and quantum chemistry. This Wiki represents a community of scientists with interests in the phase space quantum mechanics - and acts as a platform for summarizing the recent development and application of the Wigner formalism to a broad class of problems.
The most recent advances are presented in the individual profiles of the researchers in the People Section of this Wiki.