WIGNER FUNCTION — SEMICLASSICAL PHASE SPACE

Quantum Phase-Space Distribution · Moyal Bracket · Tunneling Signatures

QUANTUM STATE

DYNAMICS

OBSERVABLES

⟨x⟩: 0.000
⟨p⟩: 0.000
Δx: 0.000
Δp: 0.000
ΔxΔp: 0.000
W(x,p)≥-2/h (non-classical)
The Wigner function is the unique real phase-space quasi-distribution for QM. Negative regions signal non-classicality. Evolution obeys the Moyal equation — Liouville + quantum corrections (Moyal bracket). Tunneling appears as interference fringes.
Top: W(x,p) phase space   Bottom: marginals ρ(x) and ρ(p)