Shape invariance through Crum transformation

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dc.creatorOrganista, Jose Orlando
dc.creatorNowakowski, M.
dc.creatorRosu, H. C.
dc.date2006-03-23
dc.date2006-12-11
dc.date.accessioned2026-07-07T10:46:37Z
dc.date.available2026-07-07T10:46:37Z
dc.descriptionWe 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
dc.description26 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
dc.identifierhttps://arxiv.org/abs/math-ph/0603056
dc.identifierhttp://arxiv.org/abs/math-ph/0603056
dc.identifierJ.Math.Phys.47:122104,2006
dc.identifierdoi:10.1063/1.2397556
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183296
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.titleShape invariance through Crum transformation
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