In this paper, we consider the rational extensions of two different classes of PT symmetric complex potentials namely the asymptotically vanishing Scarf II and asymptotically non-vanishing Rosen–Morse II [ RM-II] and obtain the accompanying bound state eigenfunctions in terms of the exceptional Xm Jacobi polynomials and a certain class of orthogonal polynomials. By considering the asymptotic behavior of the exceptional polynomials, we also derive the reflection and transmission amplitudes for them and discuss the various novel properties of the corresponding amplitudes. © 2016 Elsevier Inc.

Bijan Kumar Bagchi

Physics

(SoNS) School of Natural Sciences

Kumari N.

Yadav R.K.

Khare A.

Mandal B.P.

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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

The scattering amplitude for rationally extended shape invariant Eckart potentials

Scattering amplitudes for multi-indexed extensions of solvable potentials

Journal of Physics A: Mathematical and Theoretical

Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials

Scattering amplitudes for the rationally extended PT symmetric complex potentials