Quasistationary quasi-energy states and convergence of perturbation series in a monochromatic field

To investigate the decay of a quantum system under the influence of an alternating external field, we develop a method of quasistationary quasi-energy states, whose complex quasi-energies and wave functions are obtained as the poles and residues of the wave functions of quasi-energy states of the continuum in the complex plane of the energy, The various forms of expression and the analytic properties of the integral equations for the quasistationary quasi-energy states are investigated. On the basis of an exact solution to a model problem and the general equations for the quasistationary quasi-energy states it is established that the perturbation series for the complex quasi-energy converge, and simple estimates are obtained for the radius of convergence.