Wigner Quasi-Probability Distribution
The Wigner function W(x,p) is the quantum analog of a classical phase-space distribution — but it can go negative!
Wigner Function: W(x,p) = (1/πℏ)∫ψ*(x+y)ψ(x-y)e^(2ipy/ℏ)dy
Negative regions (blue) are a signature of non-classical quantum states. For coherent states (most classical), W is Gaussian and non-negative. Fock states |n⟩ show concentric rings of negativity. Schrödinger cat states display interference fringes between two blobs.