Hi all!(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Neutrino Oscillation Formula

Tags:

**Physics Forums | Science Articles, Homework Help, Discussion**