A connection between supersymmetric quantum mechanics and Painlevé V equation

International Conference on 'Quantum Control, Exact or Perturbative, Linear or Nonlinear' to celebrate 50 years of the scientific career of Professor Bogdan Mielnik

Bermudez, D.^1,2 ; Fernández C, David J.^2

Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot

76100, Israel^1

Departamento de Física, Cinvestav, A.P. 14-740, México D.F.

07000, Mexico^2

关键词: Heisenberg algebras;    Nonlinear differential equation;    Painleve;    Second orders;    Supersymmetric quantum mechanics;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/624/1/012012/pdf
DOI  :  10.1088/1742-6596/624/1/012012

来源: IOP

【 摘 要 】

In this article we introduce the relation between supersymmetric quantum mechanics (SUSY QM) and a second-order non-linear differential equation known as Painleve V (PV) equation. To that end, we will first make a swift examination on the SUSY QM treatment of the radial oscillator and we will revisit its relation with the polynomial Heisenberg algebras (PHA). After that, we will formulate a theorem that connects SUSY QM to a set of solutions of the PV equation through specific PHA.