Infinitely many shape invariant potentials and new orthogonal polynomials

Abstract

Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the trigonometric/hyperbolic Pöschl-Teller potentials in terms of their degree \ell polynomial eigenfunctions. We present the entire eigenfunctions for these Hamiltonians (\ell=1,2,...) in terms of new orthogonal polynomials. Two recently reported shape invariant potentials of Quesne and Gómez-Ullate et al's are the first members of these infinitely many potentials.

4 pages; published in Phys.Lett.B, two references and comments added, eqs.(34)(35)(45)(46) simplified

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