Quantum Harmonic Oscillator — Wigner Function

The Wigner function W(x,p) is a quasi-probability distribution over phase space. For energy eigenstates |n⟩, W can go negative — a signature of non-classical behavior. The n=0 state is a Gaussian (coherent = classical-like). Higher n show interference fringes. Coherent states |α⟩ are Gaussians displaced in phase space, rotating with frequency ω.

Color: blue = negative Wigner values (classically forbidden) | gold = positive | White dashed = classical orbit