deletions | additions       diff --git a/section_Discussion_We_analyzed_our__.tex b/section_Discussion_We_analyzed_our__.tex  index a02ed99..ffb0771 100644  --- a/section_Discussion_We_analyzed_our__.tex  +++ b/section_Discussion_We_analyzed_our__.tex 
...
\section{Discussion}  We analyzed our results for Doppler spectroscopy buy comparing our calculated difference in frequency between the transition from the F=2 excited state of the $5^{2}S_{1/2}$ state of rubidium 87 to the $5^{2}P_{3/2}$ state and the transition from the F=3 excited state of the $5^{2}S_{1/2}$ state of rubidium 85 to the $5^{2}P_{3/2}$ state, which we found to be $1.062 x 10^{9}$ Hz $\pm$ $1.6 x 10^{7}$ Hz, compared to the value from Steck (2001, 2008) \cite{Steck_2001}  of $1.22039 x 10^{9}$ Hz $\pm$ $2 x 10^{4}$ Hz. These values are not consistent within uncertainty, but we believe there is more error than was accounted for in the fitting, as will be explained below. The reason we could only use these transitions are that they are the only ones that were on the same frequency scan. We could also analyze our results by calculating the temperature of the atoms, which should be about 300 K. However, we found temperature to be 340 K $\pm$ 40 K. This is consistent with what we expect, though just barely. However, we would actually expect the calculated temperature to be high because we fit to a Gaussian curve, even though our absorption would be a convolution between a Gaussian and a Lorentzian. \par For saturation absorption spectroscopy, we could not do a frequency calibration due to the previously mentioned bad resolution of the wavemeter. However, by taking the ratio $\frac{\delta t}{\delta \omega}$ between consecutive hyperfine peaks, we could see if that ratio was consistent within uncertainty and plot the ratios to see if we could see evidence of a nonlinear frequency scan. Our ratios were not consistent within uncertainty, likely due in part to a large underestimation of the uncertainty in our fits by Mathematica as well as a nonlinear frequency scan, for which we found evidence.  \par One major source of our error is that it is very likely we did not have a linear frequency scan. We modeled our frequency scan as a triangle wave that had the same slope for the ramp up and the ramp down, but that could very likely not be the case. For example, we could see on one of our frequency scan fits that one of our maxima and minima did not match up with where the fit put its maxima and minima.