User:Corribus/Sandbox

My Sandbox - Just for messin' around

${\overrightarrow{M}}_{l\to u}=\int {\mathrm{\Psi }}_u^{*}\overrightarrow{\mu }{\mathrm{\Psi }}_{l}d\tau$

Even in the absense of vibronic coupling and spin-orbit coupling, which is not a great assumption for most polyatomic molecules,

$\mathrm{\Psi }\approx {\psi }_{el}{\psi }_v{\psi }_r$

and

${\overrightarrow{M}}_{l\to u}={\overrightarrow{R}}_e{S}_J{q}_{v^u{v}^l}$

where

${\overrightarrow{R}}_e=\int {\psi }_{e{l}^u}^{*}\overrightarrow{\mu }{\psi }_{e{l}^l}d\tau$ (Change in electronic dipole)

$q_{v^u{v}^l}=\int {\psi }_{v^u}^{*}{\psi }_{v^l}d\tau$ (Franck-Condon factor)

and $S_J=\int {\psi }_{r^u}^{*}{\psi }_{r^l}d\tau$ (Honl-London factor)