- #1

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Hi all!

I am not sure how to prove mathematically that the expression for the probability that a neutrino originally of flavor α will later be observed as having flavor β

[itex]P_{α \rightarrow β}=\left|<\nu_{\beta}|\nu_{\alpha}(t)>\right|^2=\left|\sum_{i}U_{β i}^*U_{α i}e^{-iE_it}\right|^2[/itex] (1)

can be equivalently written as

[itex]P_{α \rightarrow β}=δ_{αβ}-4\sum_{i>j}Re(U_{β i}^*U_{α i}U_{β j}U_{α j}^*)\sin^2(\frac{Δm_{ij}^2L}{4E})+2\sum_{i>j}Im(U_{β i}^*U_{α i}U_{β j}U_{α j}^*)\sin(\frac{Δm_{ij}^2L}{4E})[/itex] (2)

Whoever is not familiar with the notation and would still like to contribute "mathematically", all the variables and constants are explained perfectly in the wiki article: http://en.wikipedia.org/wiki/Neutrino_oscillation

The proof has to be trivial, but here I am trying for two hours and still not able to show this for a general case.

I am not sure how to prove mathematically that the expression for the probability that a neutrino originally of flavor α will later be observed as having flavor β

[itex]P_{α \rightarrow β}=\left|<\nu_{\beta}|\nu_{\alpha}(t)>\right|^2=\left|\sum_{i}U_{β i}^*U_{α i}e^{-iE_it}\right|^2[/itex] (1)

can be equivalently written as

[itex]P_{α \rightarrow β}=δ_{αβ}-4\sum_{i>j}Re(U_{β i}^*U_{α i}U_{β j}U_{α j}^*)\sin^2(\frac{Δm_{ij}^2L}{4E})+2\sum_{i>j}Im(U_{β i}^*U_{α i}U_{β j}U_{α j}^*)\sin(\frac{Δm_{ij}^2L}{4E})[/itex] (2)

Whoever is not familiar with the notation and would still like to contribute "mathematically", all the variables and constants are explained perfectly in the wiki article: http://en.wikipedia.org/wiki/Neutrino_oscillation

The proof has to be trivial, but here I am trying for two hours and still not able to show this for a general case.

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