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

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

2009-11-18

arxiv.org/abs/0911.3442v1

Phys.Lett.B684:173-176,2010

Physics

Mathematical Physics

4 pages

Scientific paper

10.1016/j.physletb.2009.12.062

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.

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