Orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics

Details Orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics Orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics

2003-06-02

arxiv.org/abs/quant-ph/0306012v2

Physics

Quantum Physics

10 pages, LaTeX2e in IOP style

Scientific paper

10.2478/BF02476425

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated special functions and the corresponding raising/lowering operators. The considered equations are directly related to some Schrodinger type equations (Poschl-Teller, Scarf, Morse, etc), and the defined special functions are related to the corresponding bound-state eigenfunctions.

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