A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog

Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant curvature, the deformation parameter being related with the cur...

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Published in:Symmetry, integrability and geometry, methods and applications integrability and geometry, methods and applications, 2007-01, Vol.3, p.030
Main Author: Cariñena, José F.
Format: Article
Language:English
Subjects:
deformed oscillator
Hamilton-Jacobi separability
Hamilton-Jacobi super-separability
integrability
quantum solvable systems
super-integrability
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description Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant curvature, the deformation parameter being related with the curvature. In this sense these systems are to be considered as a harmonic oscillator and a Smorodinsky-Winternitz system in such bi-dimensional spaces of constant curvature. The quantization of the first system will be carried out and it is shown that it is super-solvable in the sense that the Schrödinger equation reduces, in three different coordinate systems, to two separate equations involving only one degree of freedom.
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subjects deformed oscillator
Hamilton-Jacobi separability
Hamilton-Jacobi super-separability
integrability
quantum solvable systems
super-integrability
title A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
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