Two-level radiative systems and perturbation theory

Abstract

We obtain expressions for the radiative level shifts of a two‐level system in terms of (i) recurrence relations, (ii) ratios of determinants, (iii) continued fractions, and (iv) a Lidstone expansion. These expressions are shown to be very useful for numerical computations. It is pointed out that perturbation series in powers of the coupling constant are not the most appropriate way of representing the solutions of the problem, but if they are to be used, different series should be employed depending on the relative value of the frequency of the field to the frequency of the two‐level system. The significance of these results in the general theory of perturbation is discussed.