Supersymmetric Quantum Mechanics and Painlev\'e IV Equation
Mathematical Physics
2011-12-14 v4 High Energy Physics - Theory
math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1012.0290,
title = {Supersymmetric Quantum Mechanics and Painlev\'e IV Equation},
author = {David Bermudez and David J. Fernández C},
journal= {arXiv preprint arXiv:1012.0290},
year = {2011}
}
Comments
Proceedings of the Workshop 'Supersymmetric Quantum Mechanics and Spectral Design' (July 18-30, 2010, Benasque, Spain)