deletions | additions       diff --git a/We_expect_the_transmission_data__.tex b/We_expect_the_transmission_data__.tex  index 7cbb336..c6502df 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}}))+offset T(\omega)=(\frac{\Gamma}{2}^{2})*((\frac{A_{1}}{(\omega-\omega_{1})^{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}