English

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

Mathematical Physics 2011-10-03 v1 math.MP Quantum Physics

Abstract

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.

Keywords

Cite

@article{arxiv.1007.4326,
  title  = {Exact spectrum for quantum oscillator in spaces of constant curvature from WKB-quantization},
  author = {E. M. Ovsiyuk and V. M. Red'kov},
  journal= {arXiv preprint arXiv:1007.4326},
  year   = {2011}
}

Comments

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