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Paper detail

Supersymmetric Quantum Mechanics and Painlevé IV Equation

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.

preprint2011arXivOpen access
David BermudezDavid J. Fernández C
math-phmath.MPhep-thquant-ph
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David BermudezDavid J. Fernández C

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