Exact solutions of the equation for composite scalar particles in quantized electromagnetic waves

Abstract

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.