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arxiv: 0911.3442 · v1 · pith:3TPPPCRQnew · submitted 2009-11-18 · 🧮 math-ph · hep-th· math.CA· math.MP· nlin.SI· quant-ph

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

classification 🧮 math-ph hep-thmath.CAmath.MPnlin.SIquant-ph
keywords polynomialspotentialslaguerreinfinitelyjacobiknownmanycorresponding
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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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