The quantum harmonic oscillator on the sphere and the hyperbolic plane
- Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid (Spain)
A nonlinear model of the quantum harmonic oscillator on two-dimensional space of constant curvature is exactly solved. This model depends on a parameter {lambda} that is related with the curvature of the space. First, the relation with other approaches is discussed and then the classical system is quantized by analyzing the symmetries of the metric (Killing vectors), obtaining a {lambda}-dependent invariant measure d{mu}{sub {lambda}} and expressing the Hamiltonian as a function of the Noether momenta. In the second part, the quantum superintegrability of the Hamiltonian and the multiple separability of the Schroedinger equation is studied. Two {lambda}-dependent Sturm-Liouville problems, related with two different {lambda}-deformations of the Hermite equation, are obtained. This leads to the study of two {lambda}-dependent families of orthogonal polynomials both related with the Hermite polynomials. Finally the wave functions {psi}{sub m,n} and the energies E{sub m,n} of the bound states are exactly obtained in both the sphere S{sup 2} and the hyperbolic plane H{sup 2}.
- OSTI ID:
- 21077639
- Journal Information:
- Annals of Physics (New York), Vol. 322, Issue 10; Other Information: DOI: 10.1016/j.aop.2006.10.010; PII: S0003-4916(06)00235-1; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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