Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials

Abstract

Exactly solvable rationally-extended radial oscillator potentials, whose wavefunctions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of $k$th-order supersymmetric quantum mechanics, with special emphasis on $k=2$. It is shown that for $\mu =1$, 2, and 3, there exist exactly $\mu$ distinct potentials of $\mu$th type and associated families of exceptional orthogonal polynomials, where $\mu$ denotes the degree of the polynomial $g_{\mu }$ arising in the denominator of the potentials.

14 pages, no figure, published version

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