deletions | additions       diff --git a/oscillationTheory.tex b/oscillationTheory.tex  index 4c9ea59..d2e6602 100644  --- a/oscillationTheory.tex  +++ b/oscillationTheory.tex 
...
\begin{equation}  \begin{split}  E_{alphaalpha}^2 E_{\alpha}^2  &= p_{alpha}^2 p_{\alpha}^2  + m_{alpha}^2 m_{\alpha}^2  \\ &= p_{alpha}^2 p_{\alpha}^2  (1 + \frac{m_{alpha}^2}{p_{alphaalpha}^2}) \frac{m_{\alpha}^2}{p_{\alpha}^2})  \\ E_{alphaalpha} E_{\alpha}  &\approx p_{alpha} p_{\alpha}  \sqrt{(1 + \frac{m_{alphaalpha}^2}{p_{alphaalpha}^2})} \frac{m_{\alpha}^2}{p_{\alpha}^2})}  \\ &\approx p_{alphaalphaalpha} p_{\alpha}  (1 + \frac{m_{alphaalpha}^2}{2 p_{alphaalpha}^2}) \frac{m_{\alpha}^2}{2 p_{\alpha}^2})  \\ &\approx p_{alphaalphaalpha} p_{\alpha}  + \frac{m_{alphaalphaalpha}^2}{2 p_{alphaalpha}} \frac{m_{\alpha}^2}{2 p_{\alpha}}  \end{split}  \end{equation}