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

Abstract

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.

10 pages, LaTeX2e in IOP style

References in corpus (2)

• Temporally stable coherent states for infinite well and Pöschl-Teller potentials
• Shape invariance, raising and lowering operators in hypergeometric type equations

Cited by in corpus (9)

• Romanovski polynomials in selected physics problems
• Extending Romanovski polynomials in quantum mechanics
• A search on the Nikiforov-Uvarov formalism
• Hypergeometric type operators and their supersymmetric partners
• Quantization of rationally deformed Morse potentials by Wronskian transforms of Romanovski-Bessel polynomials
• Associated special functions and coherent states
• Connections between Romanovski and other polynomials
• Algorithm for generating new explicitly solvable Schrodinger type equations
• Systems of orthogonal polynomials defined by hypergeometric type equations