Approximate Analytical Solutions for Two-State Time-Dependent Problems

摘要

We derive approximate analytical solutions for a class of two-state dynamical problems in which the states can differ in energy and are coupled by a time-dependent potential. These have many applications, of which atomic laser coupling (ALC) and resonant charge transfer (RCT) are specific important examples. Two types of solutions are considered: Solutions derived from perturbative Lie-algebra techniques and series solutions based on a substitution in the original equations. Examples are presented and compared with numerical solutions. It is found that the simple Lie-algebraic solutions are more useful for low-energy RCT and ALC and are valid for slowly varying potentials 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 obtained from just a few terms in the expansion.