Shape invariance through Crum transformation
Mathematical Physics
2008-11-26 v4 High Energy Physics - Theory
math.MP
Abstract
We show in a rigorous way that Crum's result on equal eigenvalue spectrum of Sturm-Liouville problems can be obtained iteratively by successive Darboux transformations. It can be shown that all neighbouring Darboux-transformed potentials of higher order, u_{k} and u_{k+1}, satisfy the condition of shape invariance provided the original potential u does. We use this result to proof that under the condition of shape invariance the n-th iteration of the original Sturm-Liouville problem defined through shape invariance is equal to the n-th Crum transformation
Keywords
Cite
@article{arxiv.math-ph/0603056,
title = {Shape invariance through Crum transformation},
author = {Jose Orlando Organista and M. Nowakowski and H. C. Rosu},
journal= {arXiv preprint arXiv:math-ph/0603056},
year = {2008}
}
Comments
26 pp, one more reference, J.-M. Sparenberg and D. Baye, J. Phys. A 28, 5079 (1995), has been added as Ref. 18 in the published version, which has 47 refs