XXXIV Workshop on Geometric Methods in Physics 28.06-4.07.2015

David J. Fernández

Painlevé equations and SUSY QM

An algorithm to generate solutions to the Painlevé IV and V equation will be introduced, which is based on supersymmetric quantum mechanics applied to the harmonic and radial oscillators respectively. The corresponding solutions turn out to be expressed in terms of confluent hypergeometric functions, which include some solution hierarchies associated to more specific special functions they are related with.

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