Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials
Mathematical Physics
2015-07-29 v2 math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
We construct rational extensions of the Darboux-P\"oschl-Teller and isotonic potentials via two-step confluent Darboux transformations. The former are strictly isospectral to the initial potential, whereas the latter are only quasi-isospectral. Both are associated to new families of orthogonal polynomials, which, in the first case, depend on a continuous parameter. We also prove that these extended potentials possess an enlarged shape invariance property.
Keywords
Cite
@article{arxiv.1503.07747,
title = {Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials},
author = {Yves Grandati and Christiane Quesne},
journal= {arXiv preprint arXiv:1503.07747},
year = {2015}
}