  We study solutions of the equation which describes the evolution of a
neutrino propagating in dense homogeneous medium in the framework of the
quantum field theory. In the two-flavor model the explicit form of Green
function is obtained, and as a consequence the dispersion law for a neutrino in
matter is derived. It is shown that there exist both the solutions describing
the stationary states and the solutions describing the spin-flavor coherent
states of the neutrino. The stationary states may be different from the mass
eigenstates, and the wave function of a state with a definite flavor should be
constructed as a linear combination of the wave functions of the stationary
states with coefficients, which depend on the mixing angle in matter. In the
ultra-relativistic limit the wave functions of the spin-flavor coherent states
coincide with the solutions of the quasi-classical evolution equation.
Quasi-classical approximation of the wave functions of spin-flavor coherent
states is used to calculate the probabilities of transitions between neutrino
states with definite flavor and helicity.
