Three neutrino oscillations in matter

Following similar approaches in the past, the Schrödinger equation for three neutrino propagation in matter of constant density is solved analytically by two successive diagonalizations of 2×2 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 (θ12 and θ13) and mass eigenvalues. In this form, the analytical results provide excellent approximation to numerical calculations and allow for simple qualitative understanding of the matter effects.