Continued fraction expressions for the eigensolutions of the hamiltonian describing the interaction between a single atom and a single field mode: comparisons with the rotating wave solutions

Formally exact continued fraction expressions for the eigenvectors and eigenvalues of the hamiltonian describing the interaction of a single atom with a single quantized field mode in the electric dipole approximation are presented. Explicit expressions for the eigen-solutions and the time-dependent properties are given in some special cases. Comparisons are made with the corresponding rotating wave solutions.