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Method of resurgent analysis in atomic collision theory. (English. Russian original) Zbl 0978.81506
Theor. Math. Phys. 112, No. 2, 1043-1055 (1997); translation from Teor. Mat. Fiz. 112, No. 2, 308-323 (1997).
Summary: We consider the atomic collision problem in the adiabatic approximation. We show that the transition probabilities can be evaluated in this approximation using the tools of resurgent analysis. We suggest a computational algorithm for the transition probabilities and give the mathematical foundation of this algorithm. The analysis is carried out using the example of two-level Landau-Zener model.
MSC:
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
81V45 Atomic physics
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