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.

4 pages

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• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
• Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials
• Properties of the Exceptional ($X_{\ell }$) Laguerre and Jacobi Polynomials

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