Supersymmetric partners of the truncated harmonic oscillator

8th International Symposium on Quantum Theory and Symmetries

David J. Fernández, C.^1 ; Morales-Salgado, V.S.^1

Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F., Mexico^1

关键词: Harmonic oscillators;    I-V equation;    Non linear;    Painleve;    Second orders;    Second-order differential equation;    Third order;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012024/pdf
DOI  :  10.1088/1742-6596/512/1/012024

来源: IOP

【 摘 要 】

First and second order supersymmetric transformations are applied to the truncated harmonic oscillator to generate new Hamiltonians with known spectra. We also study the effect of these transformations on the eigenfunctions of the initial Hamiltonian. Finally the link between first and the second order supersymmetric partners of the truncated harmonic oscillator which possess third-order differential ladder operators with the Painleve´ IV equation is used to obtain several solutions of this non-linear second-order differential equation.