Yves Grandati, Christiane Quesne, “Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials”, SIGMA, 2015, Volume 11,061, 26 pp.

This article is cited in 23 papers

Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials

Yves Grandati^a, 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

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.

Keywords: quantum mechanics; supersymmetry; orthogonal polynomials.

MSC: 81Q05; 81Q60; 42C05

Received: March 26, 2015; in final form July 15, 2015; Published online July 28, 2015

Language: English

DOI: 10.3842/SIGMA.2015.061