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Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
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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, 2010, том 6
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Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
Інший ID:
2010 Mathematics Subject Classification: 81Q60
doi:10.3842/SIGMA.2010.075
doi:10.3842/SIGMA.2010.075
Посилання:
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.
Підтримка:
This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
I am very grateful to A.A. Andrianov, F. Cannata and D.N. Nishnianidze for fruitful collaboration and many useful discussions. The work was partially supported by the RFFI grant 09-01-00145-a.
Дата:
2010
Переглядів:
302
Завантажень:
210
Анотація:
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.
