Scattering amplitudes for the rationally extended P T symmetric complex potentials

TL;DR

This paper explores rational extensions of PT symmetric complex potentials, deriving bound state solutions using exceptional Jacobi polynomials and analyzing their scattering properties, including reflection and transmission amplitudes.

Contribution

It introduces new bound state solutions for extended PT symmetric potentials using exceptional polynomials and studies their scattering characteristics.

Findings

Bound states expressed via exceptional Jacobi polynomials.

Derived reflection and transmission amplitudes for extended potentials.

Identified novel properties of scattering amplitudes.

Abstract

In this paper, we consider the rational extensions of two different P T symmetric complex potentials namely the asymptotically vanishing Scarf II and asymptotically non-vanishing Rosen-Morse II [ RM-II] potentials and obtain bound state eigenfunc- tions in terms of newly found exceptional Xm Jacobi polynomials and also some new type of orthogonal polynomials respectively. By considering the asymptotic behaviour of the exceptional polynomials, we obtain the reflection and transmission amplitudes for them and discuss the various novel properties of the corresponding amplitudes.