The ordinary position-space quantum wave function can be transformed into the momentum-space
wave function using the Fourier transform:
A similar-looking construct, but with a different interpretation, was conceived by Wigner over seventy years ago
This construct continues to interest and be useful physicists today. The function introduced by Wigner can be interpreted as a quasi- or pseudo-probability distribution corresponding to a general quantum state. The Wigner distribution allows us to study quantum correlations to classical mechanics by giving a phase-space description of quantum mechanics with a quasi-probability distribution that is joint in both x and p even though the simultaneous measurement of position and momentum violates the uncertainty principle. The Wigner function is real and integral over x (p) yields the correct momentum-space (position-space) probability density. It can be negative, however, which points to the quantum-mechanical aspects of the system. Some authors have suggested that the negative part of the Wigner function can be used to numerically describe the non-classicality of a quantum-mechanical system.