2000/03/30 by Valery G. Romanovski, Valery Romanovski, Romanovski, Valery +2
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Pulsars and Gravitational Waves Research #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #nlin.CD #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0003067
6 pages, submitted to Nonlinear Phenomena in Complex Systems (Minsk)
arxiv created 2000/03/30 · openalex publication_date 2000/03/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.