New Quantum System of Wilson Orthogonal Polynomial

TL;DR

This paper introduces a novel quantum system linked to Wilson Orthogonal Polynomials, deriving its potential function and bridging recent reformulations of quantum mechanics with traditional approaches.

Contribution

It presents a new quantum system associated with Wilson Orthogonal Polynomials and derives its potential function using matrix elements and basis functions.

Findings

Established correspondence between reformulated and conventional quantum mechanics

Derived explicit potential function for the new quantum system

Connected Wilson Orthogonal Polynomials with quantum system modeling

Abstract

We find a new quantum system associated with the Wilson Orthogonal Polynomial. In order to establish correspondence between the recent reformulation of quantum mechanic without potential function [1-2] and the convention quantum mechanics, we derived the potential function of the new quantum system using any of the proposed formulas in [4]. To achieve this, we used the matrix elements of the potential function and the basis element of the configuration space.