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 Publish in OALib Journal ISSN: 2333-9721 APC: Only $99  Views Downloads  Relative Articles Properties of the Exceptional ($X_{\ell}\$) Laguerre and Jacobi Polynomials Zeros of the exceptional Laguerre and Jacobi polynomials Two-step Darboux transformations and exceptional Laguerre polynomials The Exceptional (X_{\ell}) (q)-Racah Polynomials Admissibility condition for exceptional Laguerre polynomials Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials Exceptional Meixner and Laguerre orthogonal polynomials More...
Physics  2009

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

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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.

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