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This article is cited in 18 scientific papers (total in 18 papers)
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
José F. Cariñenaa, Manuel F. Rañadaa, Mariano Santanderb a Departamento de Física Teórica, Facultad de Ciencias
Universidad de Zaragoza, 50009 Zaragoza, Spain
b Departamento de Física Teórica, Facultad de Ciencias
Universidad de Valladolid, 47011 Valladolid, Spain
Abstract:
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.
Keywords:
deformed oscillator; integrability, super-integrability; Hamilton-–Jacobi separability; Hamilton–Jacobi super-separability; quantum solvable systems.
Received: October 31, 2006; in final form January 24, 2007; Published online February 24, 2007
Citation:
José F. Cariñena, Manuel F. Rañada, Mariano Santander, “A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog”, SIGMA, 3 (2007), 030, 23 pp.
Linking options:
https://www.mathnet.ru/eng/sigma156 https://www.mathnet.ru/eng/sigma/v3/p30
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Abstract page: | 231 | Full-text PDF : | 43 | References: | 24 |
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