Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials
نویسندگان
چکیده
Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians, which are deformations of those for the Wilson and Askey-Wilson polynomials in terms of a degree l (l = 1, 2, . . .) eigenpolynomial. These polynomials are exceptional in the sense that they start from degree l ≥ 1 and thus not constrained by any generalisation of Bochner’s theorem.
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