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

Symmetry Integrability and Geometry-Methods and Applications

article

Yves Grandati¹  Christiane Quesne² 

[1] Université de Lorraine-Site de Metz;Université Libre de Bruxelles, Campus de la Plaine CP229

关键词: quantum mechanics;    supersymmetry;    orthogonal polynomials;   

DOI  :  10.3842/SIGMA.2015.061

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown