Wigner quasiprobability distribution

For this reason, it has later been better known as the Wigner quasiprobability distribution.

The most popular in the general physics literature and historically first of these is the Wigner quasiprobability distribution, which is related to symmetric operator ordering.

In fact, it can be understood as a smoothing of the Wigner quasiprobability distribution by a Gaussian filter:

It has been shown that the Wigner quasiprobability distribution function can be regarded as an -deformation of another phase space distribution function that describes an ensemble of de Broglie-Bohm causal trajectories.

The Wigner quasiprobability distribution (also called the Wigner function or the Wigner-Ville distribution after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution.

(Sections I to IV of this article provide an overview over the Wigner-Weyl transform, the Wigner quasiprobability distribution, the phase space formulation of quantum mechanics and the example of the quantum harmonic oscillator.)