SUSY partners of the complex oscillator and Painleve IV equation

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

Fernández C, David J.^1 ; González, J.C.^1

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

07000, Mexico^1

关键词: Heisenberg algebras;    I-V equation;    Painleve;    Supersymmetry transformations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/624/1/012015/pdf
DOI  :  10.1088/1742-6596/624/1/012015

来源: IOP

【 摘 要 】

Supersymmetry transformations will be used to obtain new exactly solvable potentials from the complex oscillator. The corresponding Hamiltonians are ruled by polynomial Heisenberg algebras. By applying a mechanism to reduce to second the order of these algebras, the connection with the Painlevé IV equation is achieved, supplying us with an algorithm to generate solutions to such equation.