Theory and computational methods for studies of nonlinear phenomena in laser spectroscopy. I. General formalism

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Abstract
A general formalism will be outlined, which uses steady‐state wave functions for the study of nonlinear phenomena occurring in molecular systems interacting with intense electromagnetic fields. The steady‐state approach has the advantage of being free from the secular divergencies and normalization terms which appear in a perturbation expansion of the time‐dependent wave function. A physical interpretation of the steady states will be given by considering the interaction between the molecule and the quantized electromagnetic field. The steady states appear as states of the combined system molecule plus electromagnetic field, with eigenvalues corresponding to the energy levels of the combined system in a semiclassical approximation. Evolution operators will be introduced and used to derive formulas for n‐photon transition probabilities between molecular states both in the ordinary configuration Hilbert space and in the composite Hilbert space spanned by the steadystate wave functions.