The Hahn Quantum System

Abstract

Using a formulation of quantum mechanics based on the theory of orthogonal polynomials, we introduce a four-parameter system associated with the Hahn and continuous Hahn polynomials. The continuum energy scattering states are written in terms of the continuous Hahn polynomial whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Hahn polynomial.

arXiv comment18 pages, 7 figures

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• Establishing correspondence between the reformulation of quantum mechanics without a potential function and the conventional formulation
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Cited by in corpus (6)

• Quantum mechanics with orthogonal polynomials
• Construction of potential functions associated with a given energy spectrum -- An inverse problem. II
• Asymptotic approximations of the continuous Hahn polynomials and their zeros
• Construction of potential functions associated with a given energy spectrum
• Structural Algebraic Quantum Field Theory
• Confined systems associated with the discrete Meixner polynomials