  The equation is considered for a composite scalar particle with
polarizabilities in an external quantized electromagnetic plane wave. This
equation is reduced to a system of equations for infinite number of interacting
oscillators. After diagonalization, we come to equations for free oscillators.
As a result, exact solutions of the equation for a particle are found in a
plane quantized electromagnetic wave of the arbitrary polarization. As a
particular case, the solution for monochromatic electromagnetic waves is
considered. The relativistic coherent states of a particle are constructed in
the case of the Poisson distribution of photon numbers. In the limit when the
average photon number $<n>$ and the volume $V$ of the quantization trend to
infinity (but the photon density $<n>/V$ remains constant), the wavefunction
converts to the solution corresponding to the external classical
electromagnetic wave.
