Approximate analytical solutions for two-state time-dependent problems

We derive approximate analytical solutions for a class of two-state dynamic al problems in which the states can differ in energy and are coupled by a t ime-dependent potential. These have many applications, of which atomic lase r coupling (ALC) and resonant charge transfer (RCT) are specific important examples. Two types of solutions are considered: Solutions derived from per turbative Lie-algebra techniques and series solutions based on a substituti on in the original equations. Examples are presented and compared with nume rical solutions. It is found that the simple Lie-algebraic solutions are mo re useful for low-energy RCT and ALC and are valid for slowly varying poten tials and for both small and large values of the parameter omega, which is the energy difference between the states. In principle, the series solution can be used to give arbitrary accuracy but qualitative agreement can be ob tained from just a few terms in the expansion. (C) 1999 John Wiley & Sons, Inc.