Exact spectrum for quantum oscillator in spaces of constant curvature from WKB-quantization

Details Exact spectrum for quantum oscillator in spaces of constant curvature from WKB-quantization Exact spectrum for quantum oscillator in spaces of constant curvature from WKB-quantization

2010-07-25

arxiv.org/abs/1007.4326v1

Doklady Natsionalnoi Akademii Nauk Belarusi. 2010. 54, no 6. 38-45

Physics

Mathematical Physics

12 pages, Contrivution to BGL-7: International Conference on Non-Euclidean Geometry and its applications. 5 -- 9 July 2010, Kl

Scientific paper

Quantum-mechanical WKB-method is elaborated for the known quantum oscillator problem in curved 3-spaces models Euclid, Riemann, and Lobachevsky E_{3}, H_{3}, S_{3} in the framework of the complex variable function theory. Generalized generally covariant Schr\"{o}dinger equation is considered. In all three space models, exact energy levels are found with the help of constructing special formal WKB-sieries.

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