Quantum dynamics of a charged particle in the field of a plane electromagnetic wave in a medium at the strong bond

In the scope of relativistic quantum theory the nonlinear interaction of a charged particle with a coherent electromagnetic wave in a dielectric medium at the strong bond of the 'particle-wave' is considered. It is shown that in contrast to the case of the weak bond of the 'particle-wave' when the band structure of the particle's bound states in the wave takes place. The spectrum at the strong bond has a discrete character and resonant radiative transitions between these states are possible