The quantum harmonic oscillator on the sphere and the hyperbolic plane: {kappa}-dependent formalism, polar coordinates, and hypergeometric functions

Journal Article · Mon Oct 15 00:00:00 EDT 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2795214· OSTI ID:21013727

Carinena, Jose F; Ranada, Manuel F; Santander, Mariano ^[1]

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1. Departmento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain)

A nonlinear model representing the quantum harmonic oscillator on the sphere and the hyperbolic plane is solved in polar coordinates (r,{phi}) by making use of a curvature-dependent formalism. The curvature {kappa} is considered as a parameter and then the radial Schroedinger equation becomes a {kappa}-dependent Gauss hypergeometric equation. The energy spectrum and the wave functions are exactly obtained in both the sphere S{sup 2} ({kappa}>0) and the hyperbolic plane H{sup 2} ({kappa}<0). A comparative study between the spherical and the hyperbolic quantum results is presented.

• OSTI ID: 21013727
• Journal Information: Journal of Mathematical Physics, Vol. 48, Issue 10; Other Information: DOI: 10.1063/1.2795214; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COORDINATES
ENERGY SPECTRA
HARMONIC OSCILLATORS
HYPERGEOMETRIC FUNCTIONS
NONLINEAR PROBLEMS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SPHERES
SPHERICAL CONFIGURATION
WAVE FUNCTIONS