Wigner Functions

Wigner functions are a distribution function on phase space that allow to represent the state of a quantum-mechanical system. They are in many ways similar to classical phase space probability distributions, but can, in contrast to these, be negative. A description of a quantum system in terms of Wigner functions is equivalent to the more widely used one in terms of density operators or wave functions, but has advantages in visualizing properties of a quantum state and in studying the quantum–classical transition.