Infinitely many shape invariant potentials and new orthogonal polynomials
نویسندگان
چکیده
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 l 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 Gómez-Ullate et al.’s are the first members of these infinitely many potentials.
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