Wigner Function — Quantum Phase Space

W(x,p) quasi-probability distribution; negative values reveal non-classical quantum states

State: Coherent Min W: -- Max W: -- Non-classical: No
About: The Wigner function W(x,p) = (1/π) ∫ ψ*(x+y)ψ(x−y)e^(2ipy) dy is a quasi-probability distribution over quantum phase space. Marginals give correct probability densities: ∫W dp = |ψ(x)|², ∫W dx = |φ(p)|². Crucially, W can be negative — a signature of non-classical states. Fock states |n⟩ and Schrödinger cat states show striking negative regions (red). Coherent states (laser light) have W ≥ 0 everywhere.