On WKB Series for the Radial Kepler Problem

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We obtain the rigorous WKB expansion to all orders for the radial Kepler problem, using the residue calculus in evaluating the WKB quantization condition in terms of a complex contour integral in the complexified coordinate plane. The procedure yields the exact energy spectrum of this Schrödinger eigenvalue problem and thus resolves the controversies around the so-called "Langer correction". The problem is nontrivial also because there are only a few systems for which all orders of the WKB series can be calculated, yielding a convergent series whose sum is equal to the exact result, and thus sheds new light to similar and more difficult problems.
6 pages, submitted to Nonlinear Phenomena in Complex Systems (Minsk)

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Chaotic Dynamics, Exactly Solvable and Integrable Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/79770

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0003067
 http://arxiv.org/abs/nlin/0003067

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arXiv