This article is cited 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

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.

MSC: 81Q60; 35G20

Received: November 30, 2010; in final form March 4, 2011; Published online March 8, 2011

Language: English

DOI: 10.3842/SIGMA.2011.025

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ArXiv: 1012.0290