Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
Quantum Physics
2009-11-13 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We construct two new exactly solvable potentials giving rise to bound-state solutions to the Schr\"odinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type 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.
Cite
@article{arxiv.0807.4087,
title = {Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry},
author = {C. Quesne},
journal= {arXiv preprint arXiv:0807.4087},
year = {2009}
}
Comments
10 pages, no figure, published version (http://stacks.iop.org/1751-8121/41/392001)