Wave Packet Dispersion

Physics: Group velocity v_g = dω/dk (energy/information speed); phase velocity v_p = ω/k (phase pattern speed). Dispersion relations: ω = ck (photons, non-dispersive); ω = ℏk²/(2m) (electrons, quadratic); ω = √(gk) (deep water gravity waves). Spreading of Gaussian packet: σ(t)² = σ₀² + (ℏt/2mσ₀)². Heisenberg uncertainty: Δx·Δk ≥ ½. A narrow packet (small Δx) requires many k components (large Δk) — wider frequency spread means faster dispersion.