Principles of Quantum Mechanics · Problem 21.6

Path Integrals—II — R. Shankar

Physics — Quantum Mechanics · path-integrals-harmonic-oscillator

Problem

Use the harmonic oscillator propagator to find the evolution of an initial Gaussian wave packet Ψ(x,0)=(mωπℏ)1/4exp⁡(−mω2ℏ(x−a)2)\Psi(x, 0) = \left(\frac{m\omega}{\pi \hbar}\right)^{1/4} \exp\left(-\frac{m\omega}{2\hbar}(x - a)^2\right) where aa is the initial displacement. Show that the packet oscillates without spreading (coherent state).

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