New rational extensions of solvable potentials with finite bound state spectrum

Using the disconjugacy properties of the Schrodinger equation, we develop a new type of generalized SUSY QM partnership which allows generating new solvable rational extensions for translationally shape invariant potentials having a finite bound state spectrum. For this we prolong the dispersion relation relating the energy to the quantum number out of the physical domain until a disconjugacy sector. By Darboux-Backlund Transformations built on these prolonged states we obtain new regular isospectral extensions of the initial potential. We give the spectra of these extensions in terms of new orthogonal polynomials and study their shape invariance properties. (C) 2012 Elsevier B.V. All rights reserved.