deletions | additions       diff --git a/oscillation theory.tex b/oscillation theory.tex  index bede4fb..3204d7b 100644  --- a/oscillation theory.tex  +++ b/oscillation theory.tex 
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Therefore, the probability to transition from one flavor state to another is given by  \begin{equation} \begin{equation}\label{eq:prob-transition}  \begin{split}  \label{eq:prob-transition}  P(\nu_{\alpha} \rightarrow \nu_{\beta}) & = \mid \langle \nu_{\alpha} \mid \nu_{\beta} (t) \rangle \mid ^2 \\  & = \mid A_{\alpha}^{*}A_{\beta} e^{-i \cdot m_{\alpha}^2 t /2E} \mid^2 \\  & \equiv \mid U_{\alpha \beta} e^{-i \cdot m_{\alpha}^2 t /2E} \mid^2