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arXiv · 1012.0290

Supersymmetric Quantum Mechanics and Painlev\'e IV Equation

David Bermudez·David J. Fernández C
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Abstract

As it has been proven, the determination of general one-dimensional Schr\"odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev\'e 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 Painlev\'e IV equation. Finally, we classify these solutions into three relevant hierarchies.

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David Bermudez, David J. Fernández C. 2010-12-01. Supersymmetric Quantum Mechanics and Painlev\'e IV Equation. https://doi.org/10.3842/sigma.2011.025

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