Nonlinear scattering processes in the presence of a quantised radiation field. I. Non-relativistic treatment

Abstract

The Hamiltonian of a non-relativistic free charged particle interacting with one quantised mode of the electromagnetic field is diagonalised exactly in dipole approximation. The diagonalisation is simpler for a circularly polarised mode, but is is shown that the case of a linearly polarised mode can be reduced to the circularly polarised 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.