Another set of infinitely many exceptional (X_{\ell}) Laguerre 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.
Keywords
Cite
@article{arxiv.0911.3442,
title = {Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:0911.3442},
year = {2010}
}
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4 pages