Abstract
The author solves the Schrodinger equation in terms of continued fractions for a system exhibiting light-induced bound-free transitions over an energy gap, without making the rotating-wave approximation. He describes the evolution of the bound state and the photoelectron spectrum by investigating the analytic properties of the Fourier transforms of the probability amplitudes. The main consequence of non-RWA transitions is a Bloch-Siegert shift of the continuum threshold, which may be comparable to RWA dynamic level shifts. At high intensities the counter-rotating wave also influences the evolution of the bound state, and gives rise to multiphoton transitions competing with RWA multiphoton transitions with an odd number of photons, but these effects are probably hard to isolate experimentally.