Complex solutions to Painleve IV equation through supersymmetric quantum mechanics
David Bermudez, David J. Fernandez C
TL;DR
This paper uses supersymmetric quantum mechanics to generate complex solutions to the Painleve IV equation with real parameters, analyzing the properties of the resulting Hamiltonians and their spectra.
Contribution
It introduces a novel method for deriving complex solutions to Painleve IV using supersymmetric quantum mechanics, expanding the solution space and understanding of associated Hamiltonians.
Findings
Complex solutions to Painleve IV obtained
Analysis of Hamiltonian algebraic structure
Characterization of eigenfunctions and spectra
Abstract
In this work, supersymmetric quantum mechanics will be used to obtain complex solutions to Painleve IV equation with real parameters. We will also focus on the properties of the associated Hamiltonians, i.e. the algebraic structure, the eigenfunctions and the energy spectra.
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