Relativistic particle in the field of waves with a nonzero proper mass

Velocities and coordinates have been found of the classical relativistic particle in the field of transverse vector wave with circular polarization and non-zero proper mass. The appropriate quantum-mechanical problem is reduced to the solution of Matheiu equation. Preliminary physical considerations related to its solution stability are developed. The quantummechanical problem is solved in quasiclassical approximation, which coincides with the exact solution if the proper mass of the wave disappears. All calculations are performed for Klein-Gordon equation, but it is shown how to take into account the spin in the Dirac case