deletions | additions       diff --git a/oscillationTheory.tex b/oscillationTheory.tex  index 841ba70..795550b 100644  --- a/oscillationTheory.tex  +++ b/oscillationTheory.tex 
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\begin{equation}  \begin{split}  \mid \nu_i (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 \\ \end{split}  \end{equation}