deletions | additions       diff --git a/Energies.tex b/Energies.tex  index b6a9a29..f2ec577 100644  --- a/Energies.tex  +++ b/Energies.tex 
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\alpha_{stnm}&=\omega_0(\gamma_{st}-\gamma_{nm})$\\  &=\omega_0\left(s\Gamma_1+t\Gamma_2-n\Gamma_1-m\Gamma_2\right)\\  &=\omega_0\left[(s-n)\Gamma_1+(t-m)\Gamma_2]\\  &=\omega_0\left[2(1-\delta_{sn})\Gamma_1+2(1-\delta_{tm})\Gamma_2]\\ &=\omega_0\left[2(1-\delta_{sn})\Gamma_1+2(1-\delta_{tm})\Gamma_2]  \end{split}  \end{equation}