  We study the systems of scalar and spinor particles with mixing emitted by
external classical sources. The particles wave functions exactly accounting for
external sources are obtained directly from the Lorentz invariant wave
equations in (3+1)-dimensional space-time. Then we discuss sources which are
localized in space and emit harmonic radiation. We obtain that the considered
scalar and spinor fields can be converted from one type to another due to the
presence of the vacuum mixing. This phenomenon is shown to be analogous to
neutrino flavor oscillations in vacuum since the calculated transition and
survival probabilities coincide with the corresponding expressions for neutrino
oscillations. When we discuss the evolution of spinor particles, the situation
of general mass matrix, which has both Dirac and Majorana mass terms, is
studied. In this case we analyze the appearance of antiparticles in the initial
particles beam. The relevance of the developed technique to the description of
neutrino flavor oscillations is examined.
