= Displaced-oscillator Franck-Condon progression
{title2=$I_\nu\propto e^{-S}S^\nu/\nu!$}
For equal-frequency harmonic ground and excited molecular potentials displaced by $\Delta Q$, the low-temperature vibrational overlap has the Poisson weights in the title, with $S=M\omega_v(\Delta Q)^2/(2\hbar)$. Optical lines occur at $E_{00}+\nu\hbar\omega_v$, apart from broadening and slowly varying electronic or optical prefactors. The normalized weights sum to one and have mean vibrational excitation $S$. Unequal frequencies, several vibrations, hot initial states and intermolecular coupling modify this simple <Franck-Condon principle> model.
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