# Three Neutrino Oscillations in Uniform Matter

## TL;DR

This paper analytically solves the three-neutrino oscillation problem in uniform matter, providing explicit formulas for oscillation probabilities with modified mixing angles and mass eigenvalues, enhancing understanding of neutrino behavior in matter.

## Contribution

It introduces an analytical solution for three-neutrino oscillations in constant matter density using successive diagonalizations, offering a clear parametric form similar to vacuum oscillations.

## Key findings

- Explicit formulas for oscillation probabilities in matter.
- Modified mixing angles and mass eigenvalues in matter.
- Simplified analytical approach for neutrino oscillations.

## Abstract

Following similar approaches in the past, the Schrodinger equation for three neutrino propagation in matter of constant density is solved analytically by two successive diagonalizations of 2x2 matrices. The final result for the oscillation probabilities is obtained directly in the conventional parametric form as in the vacuum but with explicit simple modification of two mixing angles ($\theta_{12}$ and $\theta_{13}$) and mass eigenvalues.