Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials

TL;DR

This paper introduces a new infinite family of shape invariant potentials and corresponding exceptional Laguerre polynomials, derived via a limiting process from Jacobi polynomials, expanding the set of exactly solvable quantum models.

Contribution

It presents a novel set of shape invariant potentials and exceptional Laguerre polynomials obtained through a simple limiting procedure from Jacobi polynomials.

Findings

New infinitely many shape invariant potentials.

Corresponding exceptional Laguerre polynomials derived.

Method based on limiting procedure from Jacobi polynomials.

Abstract

We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X_{\ell}) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly solvable potentials in one dimensional quantum mechanics and the corresponding X_{\ell} Laguerre and Jacobi polynomials (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417). The new X_{\ell} Laguerre polynomials and the potentials are obtained by a simple limiting procedure from the known X_{\ell} Jacobi polynomials and the potentials, whereas the known X_{\ell} Laguerre polynomials and the potentials are obtained in the same manner from the mirror image of the known X_{\ell} Jacobi polynomials and the potentials.