New rational extensions of solvable potentials with finite bound state spectrum

Details New rational extensions of solvable potentials with finite bound state spectrum New rational extensions of solvable potentials with finite bound state spectrum

2012-03-19

arxiv.org/abs/1203.4149v1

Physics

Mathematical Physics

Scientific paper

Using the disconjugacy properties of the Schr\"odinger equation, it is possible to develop a new type of generalized SUSY QM partnership which allows to generate 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. The prolonged excited states Riccati-Schr\"odinger (RS) functions are used to build Darboux-B\"acklund transforms which give 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.

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