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Approximate analytical solutions for two‐state time‐dependent problems
Author(s) -
Burrows B. L.,
Moideen F. M.,
Amos A. T.
Publication year - 1999
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1999)74:5<559::aid-qua12>3.0.co;2-w
Subject(s) - lie algebra , series (stratigraphy) , simple (philosophy) , algebraic number , state (computer science) , charge (physics) , coupling (piping) , energy (signal processing) , class (philosophy) , substitution (logic) , physics , mathematics , statistical physics , quantum mechanics , mathematical analysis , algorithm , computer science , mechanical engineering , paleontology , philosophy , epistemology , artificial intelligence , engineering , biology , programming language
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 ω, 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. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 559–571, 1999