Coherent-state overlap
= Coherent-state overlap
{title2=$\langle\beta|\alpha\rangle=e^{-(|\beta|^2+|\alpha|^2)/2+\beta^*\alpha}$}
Expand both states in the <Fock basis> and sum the exponential series to obtain the displayed overlap. In particular $\langle\alpha|-\alpha\rangle=e^{-2|\alpha|^2}$. Distinct <coherent states> are nonorthogonal at finite separation; dropping this overlap can give incorrect normalization and small-amplitude limits.