deletions | additions       diff --git a/We_expect_the_transmission_data__.tex b/We_expect_the_transmission_data__.tex  index c3af8ce..7cbb336 100644  --- a/We_expect_the_transmission_data__.tex  +++ b/We_expect_the_transmission_data__.tex 
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We expect the transmission data to theoretically be a sum of multiple Lorentzian functions. With the transitions we measure, we expect to see three hyperfine peaks. However, due to crossovers, we actually see six. Thus we can find the transition frequencies associated with the hyperfine structure of $^{85}Rb$ and $^{87}Rb$ by fitting the raw transmission data to a function comprised of six Lorentzians and an offset. The equation is given by,   \begin{equation}\label{eq1}  T(\omega)=(\frac{\Gamma}{2}^{2})*((\frac{A_{1}}{(\omega-\omega_{1})^{2}+\frac{\Gamma}{2}^{2}})+(\frac{A_{2}}{(\omega-\omega_{2})^{2}+\frac{\Gamma}{2}^{2}})+\cdots+(\frac{A_{6}}{(\omega-\omega_{6})^{2}+\frac{\Gamma}{2}^{2}})) T(\omega)=(\frac{\Gamma}{2}^{2})*((\frac{A_{1}}{(\omega-\omega_{1})^{2}+\frac{\Gamma}{2}^{2}})+(\frac{A_{2}}{(\omega-\omega_{2})^{2}+\frac{\Gamma}{2}^{2}})+\cdots+(\frac{A_{6}}{(\omega-\omega_{6})^{2}+\frac{\Gamma}{2}^{2}}))+offset  \end{equation}  Where the normal equation for a Lorentzian is,  \begin{equation}\label{eq2}  T(\omega)=(\frac{\Gamma}{2}^{2})*((\frac{A}{(\omega-\omega_{0})^{2}+\frac{\Gamma}{2}^{2}}) T(\omega)=(\frac{\Gamma}{2}^{2})*(\frac{A}{(\omega-\omega_{0})^{2}+\frac{\Gamma}{2}^{2}})  \end{equation}