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arXiv · 0807.4087

Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

C. Quesne
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Abstract

We construct two new exactly solvable potentials giving rise to bound-state solutions to the Schrödinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type $X_1$ exceptional orthogonal polynomials. These potentials, extending either the radial oscillator or the Scarf I potential by the addition of some rational terms, turn out to be translationally shape invariant as their standard counterparts and isospectral to them.

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C. Quesne. 2008-09-01. Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry. https://doi.org/10.1088/1751-8113/41/39/392001

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