Wignerfunctie

The Wigner function, also known as the Wigner quasi-probability distribution, is a mathematical tool used in quantum mechanics to represent quantum states in a way that resembles a classical probability distribution. It is a function of both position and momentum, analogous to a phase-space distribution in classical mechanics. However, unlike a true probability distribution, the Wigner function can take on negative values, indicating the presence of quantum phenomena such as interference.

Introduced by Eugene Wigner in 1932, the Wigner function provides a bridge between the quantum and classical descriptions of a system. It allows for the calculation of expectation values of observables, similar to how one would use classical probability distributions. For a pure quantum state described by a wave function ψ(x), the Wigner function W(x, p) is defined through a Fourier transform involving the wave function and its complex conjugate.

While it offers a useful visualization and computational approach, the Wigner function is not a true probability distribution because its negative values violate the axioms of probability theory. These negative regions are a hallmark of quantum superposition and entanglement, and their presence signifies quantum correlations that have no classical counterpart. Despite this, the Wigner function remains a valuable tool in various fields of quantum physics, including quantum optics, quantum information, and condensed matter physics.