Quantum Wave Packet Spreading

Initial width σ — 30

Momentum k₀ — 0.20

Potential

Barrier height V₀ — 0.5

Speed — 3

t = 0
⟨x⟩ = —
σ_x = —

Split-operator: e^{-iHΔt} ≈ e^{-iV Δt/2} · e^{-iT Δt} · e^{-iV Δt/2}. The kinetic part is diagonal in momentum space (FFT → multiply → IFFT).

Free spreading: σ(t)² = σ₀² + (t/2mσ₀)² — quantum dispersion has no classical analogue.