Quantum Harmonic Oscillator — Coherent States

A coherent state |α⟩ is a displaced vacuum: minimum-uncertainty wavepacket that oscillates like a classical particle. The probability density |ψ(x,t)|² is a Gaussian that follows the classical trajectory x(t) = 2Re(α)·cos(t).

⟨x⟩ =
⟨p⟩ =
|α| =
Δx = 0.5