User:Corribus/Sandbox

My Sandbox - Just for messin' around

${\vec {M}}_{l\rightarrow u}=\int \Psi _{u}^{*}{\vec {\mu }}\Psi _{l}\,d\tau$

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

$\Psi \approx \psi _{el}\psi _{v}\psi _{r}$

and

${\vec {M}}_{l\rightarrow u}={\vec {R}}_{e}S_{J}q_{v^{u}v^{l}}$

where

${\vec {R}}_{e}=\int \psi _{el^{u}}^{*}{\vec {\mu }}\psi _{el^{l}}\,d\tau$ (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)