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)

Cited by in corpus (2)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry