Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and shape invariance - two main ingredients of the supersymmetrical...
Збережено в:
| Дата: | 2010 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146511 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics / M.V. Ioffe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 27 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and shape invariance - two main ingredients of the supersymmetrical quantum mechanics. The first method explores the opportunity to separate variables in the supercharge, and it allows to find a part of spectrum of the Schrödinger Hamiltonian. The second method works when the standard separation of variables procedure can be applied for one of the partner Hamiltonians. Then the spectrum and wave functions of the second partner can be found. Both methods are illustrated by the example of two-dimensional generalization of Morse potential for different values of parameters. |
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