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

Abstract

The paper advances Odake and Sasaki’s idea 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 Schrödinger 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. One can extend this isospectral family of solvable rational potentials by including ‘juxtaposed’ pairs of Romanovski-Bessel polynomials into the aforementioned polynomial Wronskians which results in deleting the corresponding pairs of bound energy states.