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

The paper advances Odake and Sasaki’s idea to re-write eigenfunctions of rationally deformed Morse potentials in terms Wronskians Laguerre polynomials the reciprocal argument. It is shown that constructed quasi-rational seed solutions Schrödinger equation with potential are formed by generalized Bessel degree-independent indexes. As a new achievement we can point construction Darboux-Crum net isospectral rational using no positive zeros. One extend this family solvable including ‘juxtaposed’ pairs Romanovski-Bessel into aforementioned polynomial which results deleting corresponding bound energy states.