Supersymmetric Quantum Mechanics and Painlevé IV Equation

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.

Proceedings of the Workshop 'Supersymmetric Quantum Mechanics and Spectral Design' (July 18-30, 2010, Benasque, Spain)

References in corpus (2)

• Supersymmetric Quantum Mechanics
• Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials

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