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Complex SUSY Transformations and the Painlevé IV Equation

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Author(s): David Bermúdez

Journal: Symmetry, Integrability and Geometry : Methods and Applications
ISSN 1815-0659

Volume: 8;
Start page: 069;
Date: 2012;
Original page

Keywords: supersymmetric quantum mechanics | Painlevé equations | differential equations | quantum harmonic oscillator | polynomial Heisenberg algebras

ABSTRACT
In this paper we will explicitly work out the complex first-order SUSY transformation for the harmonic oscillator in order to obtain both real and complex new exactly-solvable potentials. Furthermore, we will show that this systems lead us to exact complex solutions of the Painlevé IV equation with complex parameters. We present some concrete examples of such solutions.
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