Wigner quasiprobability distribution

Summary

The Wigner quasiprobability distribution, or Wigner function, of a quantum state is a real function $W(x, p)$ on phase space. Its marginals are the probability densities of position and of momentum. The expectation value of an observable is the integral of its Weyl symbol against $W$. It can take negative values, so it is not a probability density; negativity is a sign of non-classical behaviour. It is the basic object of the phase space formulation of quantum mechanics, and the same transform is the Wigner distribution function of signal analysis.