Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

Author:

C Quesne  

Journal:

Journal of Physics A: General Physics

Issue Date:

2008

Abstract(summary):

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 X₁ 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.

Page:

392001 (6pp)