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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 025, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.025 (Mi sigma583) 		 
This article is cited in 37 scientific papers (total in 37 papers)

Supersymmetric Quantum Mechanics and Painlevé IV Equation

David Bermúdez, David J. Fernández C.

Departamento de Física, Cinvestav, AP 14-740, 07000 México DF, Mexico
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DOI: https://doi.org/10.3842/SIGMA.2011.025
Abstract: As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlevé IV equation. Finally, we classify these solutions into three relevant hierarchies.
Keywords: supersymmetric quantum mechanics; Painlevé equations.
Received: November 30, 2010; in final form March 4, 2011; Published online March 8, 2011
Bibliographic databases:
Document Type: Article
MSC: 81Q60; 35G20
Language: English
Citation: David Bermúdez, David J. Fernández C., “Supersymmetric Quantum Mechanics and Painlevé IV Equation”, SIGMA, 7 (2011), 025, 14 pp.
Citation in format AMSBIB
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\paper Supersymmetric Quantum Mechanics and Painlev\'e IV Equation
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    • This publication is cited in the following 37 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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