Infinitely many shape invariant potentials and new orthogonal polynomials

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 Poschl-Teller potentials in terms of their degree e polynomial eigenfunctions. We present the entire eigenfunctions for these Hamiltonians (l = 1, 2, ...) in terms of new orthogonal polynomials. Two recently reported shape invariant potentials of Quesne and Gomez-Ullate et al.'s are the first members of these infinitely many potentials. (C) 2009 Elsevier B.V. All rights reserved.