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A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
Інший ID:
2000 Mathematics Subject Classification: 37J35; 34A34; 34C15; 70H06
Посилання:
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog / J.F. Cariñena, M.F. Rañada, M. Santander // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 44 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Workshop on Geometric Aspects of Integrable Systems (July 17–19, 2006, University of Coimbra, Portugal). Partial financial support of research projects BFM-2003-02532, FPA-2003-02948, MTM-2005-09183, DGA E24/1 and VA013C05 is acknowledged.
Дата:
2007
Переглядів:
591
Завантажень:
214
Анотація:
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.
