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The motivation for neutrino oscillation was discused in section REFERENCE. To see how a neutrino acutally "oscillates," lets assume, that we have a neutrino that intially has definite flavor. That is  \begin{equation}  \mid \nu_{\alpha} (0)  \rangle = U_{\alpha i}^{*} \mid \nu_{\alpha} \nu_{\i}  \rangle \end{equation}  Where $\alpha$ ranges over (e, $\mu$, and $\tau$) and stand for the respective flavor state. And $U_{ij}$ is the corresponding element in the PMNS matrix \footnote{For more information see ***}.