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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| Дата: | 2007 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147830 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147830 |
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dspace |
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irk-123456789-1478302019-02-17T01:25:48Z A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog Cariñena, J.F. Rañada, M.F. Santander, M. 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. 2007 Article 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. 1815-0659 2000 Mathematics Subject Classification: 37J35; 34A34; 34C15; 70H06 http://dspace.nbuv.gov.ua/handle/123456789/147830 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Cariñena, J.F. Rañada, M.F. Santander, M. |
| spellingShingle |
Cariñena, J.F. Rañada, M.F. Santander, M. A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Cariñena, J.F. Rañada, M.F. Santander, M. |
| author_sort |
Cariñena, J.F. |
| title |
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog |
| title_short |
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog |
| title_full |
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog |
| title_fullStr |
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog |
| title_full_unstemmed |
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog |
| title_sort |
super-integrable two-dimensional non-linear oscillator with an exactly solvable quantum analog |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147830 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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