It is proved the equivalence of the compatibility condition of Ramos (2011, 2012) with a condition found in Yadav et al. (2015). The link of Shape Invariance with the existence of a Potential Algebra is reinforced for the rationally extended Shape Invariant potentials. Some examples on X1 and Xℓ Jacobi and Laguerre cases are given. © 2017 Elsevier Inc.

Bijan Kumar Bagchi

Physics

(SoNS) School of Natural Sciences

Ramos A.

Khare A.

Kumari N.

Mandal B.P.

Yadav R.K.

Fulltext

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Shiv Nadar University

Annals of Physics

In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex PT symmetric potentials. We focus our attention on the conventional potentials such as the generalized Pöschl Teller (GPT), Scarf-I, and PT symmetric Scarf-II which are invariant under certain parametric transformations. The resulting set of potentials is shown to yield a completely different behavior of the bound state solutions. Further, the supersymmetric partner potentials acquire different forms under such parametric transformations leading to new sets of exactly solvable real and PT symmetric complex potentials. These potentials are also observed to be shape invariant (SI) in nature.We subsequently take up a study of the newly discovered rationally extended SI potentials, corresponding to the above mentioned conventional potentials, whose bound state solutions are associated with the exceptional orthogonal polynomials (EOPs).We discuss the transformations of the corresponding Casimir operator employing the properties of the so(2,1) algebra.

Journal of Mathematical Physics

Parametric symmetries in exactly solvable real and PT symmetric complex potentials

Group theoretic approach to rationally extended shape invariant potentials

Physics Letters A

A short proof of the Gaillard–Matveev theorem based on shape invariance arguments

Extended Krein-Adler theorem for the translationally shape invariant potentials

Journal of Engineering Mathematics

Comments on the generalized SUSY QM partnership for Darboux–Pöschl–Teller potential and exceptional Jacobi polynomials

A short note on “Group theoretic approach to rationally extended shape invariant potentials” [Ann. Phys. 359 (2015) 46–54]