Shape invariance through Crum transformation
Organista, José Orlando
Rosu Barbus, Haret-Codratian
"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 neighbouring Darboux-transformed potentials of higher order, uk and uk+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."
Knowledge areaCIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA
EditorAmerican Institute of Physics
High Energy Physics - Theory