Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

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.

10 pages, no figure, published version (http://stacks.iop.org/1751-8121/41/392001)

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• Supersymmetry and Quantum Mechanics
• Supersymmetry and algebraic deformations
• New approach to (quasi)-exactly solvable Schrodinger equations with a position-dependent effective mass
• Comprehensive analysis of conditionally exactly solvable models
• A unified treatment of exactly solvable and quasi-exactly solvable quantum potentials

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