Coherent State — Minimum-Uncertainty Oscillation That Never Spreads

A displaced Gaussian bouncing in the harmonic well. σ_x·σ_p = ℏ/2 for all time. Compare to the Fock state |n⟩ at the same energy — it never moves (⟨x⟩=0 always).

|ψ(x,t)|² — wavefunction in oscillator potential

Phase space (⟨x⟩, ⟨p⟩)

|α| = 2.00 (amplitude)

Speed = 1.0×

t = 0.00 ⟨x⟩ = — x₀ ⟨p⟩ = — σ_x·σ_p = 0.500 ℏ T = 6.283 (= 2π)