Shape invariance through Crum transformation

Journal Article · Fri Dec 15 00:00:00 EST 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2397556· OSTI ID:20861550

Organista, Jose Orlando; Nowakowski, Marek; Rosu, H C ^[1]

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1. 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

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENVALUES
ITERATIVE METHODS
POTENTIALS
STURM-LIOUVILLE EQUATION
TRANSFORMATIONS