Complex SUSY Transformations and the Painlev\'e IV Equation
Mathematical Physics
2012-10-12 v2 High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
In this paper we will explicitly work out the complex first-order SUSY transformation for the harmonic oscillator in order to obtain both real and complex new exactly-solvable potentials. Furthermore, we will show that this systems lead us to exact complex solutions of the Painlev\'e IV equation with complex parameters. We present some concrete examples of such solutions.
Cite
@article{arxiv.1208.1782,
title = {Complex SUSY Transformations and the Painlev\'e IV Equation},
author = {David Bermúdez},
journal= {arXiv preprint arXiv:1208.1782},
year = {2012}
}