Construction of potential functions associated with a given energy spectrum -- An inverse problem. II

TL;DR

This paper extends the inverse spectral problem by constructing multiple potential functions linked to the same energy spectrum, focusing on Wilson polynomials and Jacobi bases, revealing new exactly solvable quantum systems.

Contribution

It introduces a method to generate additional potential functions for the same spectrum using Wilson polynomials and Jacobi bases, expanding inverse problem solutions.

Findings

Multiple potential functions for identical spectra are constructed.

New exactly solvable potentials related to Wilson polynomials are identified.

The approach broadens the class of inverse spectral problems.

Abstract

We continue our solution of the inverse problem started by the first author in [Int. J. Mod. Phys. A 35, xxxx (2020), in production]. Additional potential functions for exactly solvable problems that correspond to the same energy spectrum formula but for different energy polynomials and bases are found. In this work, we obtain a class of potential functions associated with the Wilson polynomial and "Jacobi basis".