  We propose a modified Dirac equation for a massive neutrino moving in the
presence of the background matter. The effects of the charged and
neutral-current interactions with the matter as well as the matter motion and
polarization are accounted for. In the particular case of the matter with a
constant density the exact solutions of this equation are found, the neutrino
energy spectrum in the matter is also determined. On this basis the effects of
the neutrino trapping and reflection, the neutrino-antineutrino pair
annihilation and creation in a medium are studied. The quantum theory of the
spin light of neutrino in matter ($SL\nu$) is also developed.
