A Gaussian wave packet ψ(x,0) = e^(−x²/2σ²)e^(ik₀x) evolves under ω(k). Watch group velocity (envelope) vs phase velocity (carrier), and see how dispersion spreads the packet.
Dispersion Type
v_g = —
v_p = —
Width: —
Group vs Phase Velocity
v_p = ω/k (phase)
v_g = dω/dk (group)
Normal dispersion: v_g < v_p
Anomalous: v_g > v_p
Schrödinger: σ(t)² = σ₀² + t²/σ₀² — linear spreading in time.