Approximate solutions to the neutrino oscillation problem in matter

In this paper, we present approximate solutions to the neutrino evolution equation, calculated by different methods. In a two-neutrino framework, we compute the transition probability by using numerical methods, series solutions, and by taking the neutrino evolution operator as a product of ordered partial operators. This procedure is applied to linearly and sinusoidally varying matter densities just as illustrative examples, using the physical parameters, which produce the main effects on neutrino oscillations from ν e to other flavors for L ≃3000 Km and E ≃1 GeV. The evolution operator as a product of partial operators in the three-neutrino case is obtained. We compare the results and discuss the extension to an arbitrary density profile.