= Quantum occupation scale of a classical oscillator
{title2=$\bar n\simeq m\omega A^2/(2\hbar)$}
A classical oscillator of amplitude $A$ has <energy> $m\omega^2A^2/2$. Comparing with the oscillator spacing $\hbar\omega$ gives the large-occupation scale displayed. A <coherent state> with this classical amplitude has exactly this <mean> excitation occupation and a Poisson number distribution; its total <mean> <energy> also includes the zero-point term. An observed macroscopic amplitude does not, by itself, establish a pure <coherent state>.
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