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

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dc.creatorCariñena, José F.
dc.creatorRañada, Manuel F.
dc.creatorSantander, Mariano
dc.date2007-02-24
dc.date.accessioned2026-07-07T09:34:27Z
dc.date.available2026-07-07T09:34:27Z
dc.descriptionTwo 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.
dc.descriptionThis is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0702084
dc.identifierhttp://arxiv.org/abs/math-ph/0702084
dc.identifierSIGMA 3 (2007), 030, 23 pages
dc.identifierdoi:10.3842/SIGMA.2007.030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159500
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleA Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
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