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SIGMA 11 (2015), 061, 26 pages arXiv:1503.07747
https://doi.org/10.3842/SIGMA.2015.061
Contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials
Yves Grandati a and Christiane Quesne b
a) Equipe BioPhysStat, LCP A2MC, Université de Lorraine-Site de Metz, 1 bvd D.F. Arago, F-57070, Metz, France
b) Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium
Received March 26, 2015, in final form July 15, 2015; Published online July 28, 2015
Abstract
We construct rational extensions of the Darboux-Pöschl-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.
Key words:
quantum mechanics; supersymmetry; orthogonal polynomials.
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