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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 075, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.075
(Mi sigma533)
 

This article is cited in 20 scientific papers (total in 20 papers)

Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics

Mikhail V. Ioffe

Saint-Petersburg State University, St.-Petersburg, 198504 Russia
References:
Abstract: 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.
Keywords: supersymmetry; separation of variables; integrability; solvability.
Received: August 24, 2010; in final form September 19, 2010; Published online September 24, 2010
Bibliographic databases:
Document Type: Article
MSC: 81Q60
Language: English
Citation: Mikhail V. Ioffe, “Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics”, SIGMA, 6 (2010), 075, 10 pp.
Citation in format AMSBIB
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  • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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