Confluent chains of DBT: enlarged shape invariance and new orthogonal polynomials

Yves Grandati, Christiane Quesne

Published 2015-03-26Version 1

We construct rational extensions of the Darboux-P\"{o}schl-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.