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

$$\vec M_{l \rightarrow u}= \vec R_eS_Jq_{v^uv^l}$$

where

$$\vec R_e=\int \psi_{el^u}^* \vec \mu \psi_{el^l} \,d \tau $$ (Change in electronic dipole)

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

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