Shape invariance through Crum transformation
Journal Article
·
· Journal of Mathematical Physics
- Departamento de Fisica, Universidad de los Andes, Cra.1E No. 18A-10, Santafe de Bogota (Colombia)
We show in a rigorous way that Crum's result regarding the equal eigenvalue spectrum of Sturm-Liouville problems can be obtained iteratively by successive Darboux transformations. Furthermore, it can be shown that all neighboring Darboux-transformed potentials of higher order, u{sub k} and u{sub k+1}, satisfy the condition of shape invariance provided the original potential u does so. Based on this result, we prove that under the condition of shape invariance, the nth iteration of the original Sturm-Liouville problem defined solely through the shape invariance is equal to the nth Crum transformation.
- OSTI ID:
- 20861550
- Journal Information:
- Journal of Mathematical Physics, Vol. 47, Issue 12; Other Information: DOI: 10.1063/1.2397556; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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