  We find the solution to the Dirac equation for a massive neutrino with a
magnetic moment propagating in background matter and interacting with the
twisting magnetic field. In frames of the relativistic quantum mechanics
approach to the description of neutrino evolution we use the obtained solution
to derive neutrino wave functions satisfying the given initial condition. We
apply the results to the analysis of neutrino spin oscillations in matter under
the influence of the twisting magnetic field. Then on the basis of the yielded
results we describe spin-flavor oscillations of Dirac neutrinos that mix and
have non-vanishing matrix of magnetic moments. We again formulate the initial
condition problem, derive neutrinos wave functions and calculate the transition
probabilities for different magnetic moments matrices. The consistency of the
obtained results with the quantum mechanical treatment of spin-flavor
oscillations is discussed. We also consider several applications to
astrophysical and cosmological neutrinos.
