Algebraic Approach to Shape Invariance

Abstract

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite-dimensional. The conditions under which they become finite-dimensional are explored.

Submitted to Physical Review A. Latex file, 9 pages. Manuscript is also available at http://nucth.physics.wisc.edu/preprints/

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