A continued fraction solution to the problem of a single atom interacting with a single radiation mode in the electric dipole approximation

Difference equations are derived for the Laplace transforms of the time dependent probability amplitudes of a system consisting of a single photon interacting with a single two-level atom in the electric dipole approximation. Formally exact continued fraction solutions of these difference equations are obtained and applied to the problems of stimulated and spontaneous emission and absorption of radiation.