Quantization of rationally deformed Morse potentials by Wronskian transforms of Romanovski-Bessel polynomials

TL;DR

This paper develops a novel method for quantizing rationally deformed Morse potentials using Wronskians of Romanovski-Bessel and generalized Bessel polynomials, leading to new isospectral potentials.

Contribution

It introduces a new approach to express eigenfunctions of deformed Morse potentials via Wronskians of special polynomials, expanding the tools for solving quantum systems.

Findings

Constructed quasi-rational seed solutions with degree-independent indexes.

Built Darboux-Crum nets of isospectral potentials using Wronskians.

Re-expressed rational Darboux-Crum transforms in terms of special polynomials.

Abstract

The paper advances the suggestion by Odake and Sasaki to re-write eigenfunctions of rationally deformed Morse potentials in terms of Wronskians of Laguerre polynomials in the reciprocal argument. It is shown that the constructed quasi-rational seed solutions of the Schrodinger equation with the Morse potential are formed by generalized Bessel polynomials with degree-independent indexes. As a new achievement we can point to the construction of the Darboux-Crum net of isospectral rational potentials using Wronskians of generalized Bessel polynomials with no positive zeros. It was then proved that any solvable rational Darboux-Crum transform of the Morse potential can be re-expressed in terms of Wronskians of the latter polynomials accompanied by juxtaposed pairs of Romanovski-Bessel polynomials.