A Modern Approach to Quantum Mechanics · Problem 7.21

Path Integrals — John S. Townsend

Physics — Quantum Mechanics · coherent-states-translation-expectation

Problem

Verify that

\langle x\rangle = d\cos\omega t

for the coherent state

\hat{T}(d)|0\rangle

that is generated by translating the ground state

|0\rangle

of the harmonic oscillator by a distance

d