Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey–Wilson polynomials

摘要

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 ( = 1, 2, . . .) eigenpolynomial. These polynomials are exceptional in the sense that they start from degree 1 and thus not constrained by any generalisation of Bochner’s theorem.