The Wilson-Racah Quantum System

TL;DR

This paper introduces a novel quantum system characterized by Wilson and Racah polynomials, linking scattering states and bound states to these polynomials within a potential-free quantum framework.

Contribution

It presents a new four-parameter quantum system using a potential-free formulation, connecting Wilson and Racah polynomials to scattering and bound states.

Findings

Continuum states described by Wilson polynomials with scattering phase shifts.

Discrete bound states associated with Racah polynomials.

Novel formulation without potential functions.

Abstract

Using a recent formulation of quantum mechanics without potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics gives the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials. We are honored to dedicate this work to Prof. Hashim A. Yamani on the occasion of his 70th birthday.