Nonlinear scattering processes in the presence of a quantized radiation field Pt. 1

The Hamiltonian of a nonrelativistic free charged particle interacting with one quantized mode of the electromagnetic field is diagonalized exactly in dipole approximation. The diagonalization is simpler for a circularly polarized mode but it is shown that the case of a linearly polarized mode can be reduced to the circularly polarized one. Exact stationary and time dependent states of this Hamiltonian are then calculated. Based on these results the rederivation of the nonlinear inverse and direct bremsstrahlung's cross section is presented and the connection with earlier (semiclassical) approaches is also established. Photon number distribution functions for different initial conditions are also determined in analytical form. (author)