Approximate analytical solutions for two-state time-dependent problems

✍ Scribed by B. L. Burrows; F. M. Moideen; A. T. Amos

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 254 KB
• Volume: 74
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1999)74:5<559::aid-qua12>3.0.co;2-w

✦ Synopsis

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 Ž . Ž . 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 , 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.