Symmetries and the compatibility condition for the new translational shape invariant potentials
arXiv:1205.0712 · doi:10.1016/j.physleta.2012.10.033
Abstract
In this letter we study a class of symmetries of the new translational extended shape invariant potentials. It is proved that a generalization of a compatibility condition introduced in a previous article is equivalent to the usual shape invariance condition. We focus on the recent examples of Odake and Sasaki (infinitely many polynomial, continuous and multi-index rational extensions). As a byproduct, we obtain new relations, to the best of our knowledge, for Laguerre, Jacobi polynomials and (confluent) hypergeometric functions.
arXiv comment15 pages, no figures, revised version to appear in Physics Letters A
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- Extensions of solvable potentials with finitely many discrete eigenstates
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