deletions | additions       diff --git a/oscillationTheory.tex b/oscillationTheory.tex  index 393ff6a..d810332 100644  --- a/oscillationTheory.tex  +++ b/oscillationTheory.tex 
...
\end{split}  \end{equation}  Plugging this into our expression for $\mid \nu_{i}(x, \nu_{\alpha}(x,  t) \rangle$ \begin{equation}  \begin{split}  \mid \nu_i \nu_{\alpha}  (x, t) \rangle &= A e^{- i (E_i t - \vec{p_i} \cdot \vec{x})} \mid \nu_i (0) \rangle \\ &= A e^{-i(p_{i} + \frac{m_{i}^2}{2 E})t} e^{- \vec{p_i} \cdot \vec{x}} \mid \nu_{i}(0) \rangle \\  &= A e^{- i E_i t}e^{i (E_{i} - \frac{m_{i}^2}{2 E}) \cdot \vec{x})} \mid \nu_{i}(0) \rangle \\   &\approx A e^{- i E_i t}e^{ -i \frac{m_{i}^2}{2 E} \cdot \vec{x}} \mid \nu_{i}(0) \rangle \\