Factorization method for the truncated harmonic oscillator

30th International Colloquium on Group Theoretical Methods in Physics

Fernandez, D.J.^1 ; Morales-Salgado, V.S.^1

Departamento de Fisica, Cinvestav, A.P. 14-740, Mexico D.F

07000, Mexico^1

关键词: Factorization methods;    Fourth order;    Harmonic oscillators;    Non linear;    Painleve;    Potential barriers;    Second orders;    Second-order differential equation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012035/pdf
DOI  :  10.1088/1742-6596/597/1/012035

来源: IOP

【 摘 要 】

Factorization procedures of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. Certain systems obtained in a straightforward way through said method possess differential ladder operators of both types, third and fourth order. Since systems with this kind of operators are linked with the Painleve IV and V equations respectively, several solutions of these non-linear second-order differential equations will be simply found.