A Modern Approach to Quantum Mechanics · Problem 14.7

Photons and Atoms — John S. Townsend

Physics — Quantum Mechanics · coherent-state-photon-distribution

Problem

Show that the distribution of photons in a coherent state ∣α⟩=e−∣α∣2/2∑nk,s=0∞αnk,snk,s!∣nk,s⟩|\alpha\rangle = e^{-|\alpha|^2/2}\sum_{n_{\mathbf{k},s}=0}^\infty \frac{\alpha^{n_{\mathbf{k},s}}}{\sqrt{n_{\mathbf{k},s}!}}|n_{\mathbf{k},s}\rangle is a Poisson distribution with ⟨nk,s⟩=∣α∣2\langle n_{\mathbf{k},s}\rangle = |\alpha|^2.

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