A class of exactly solvable rationally extended non-central potentials in Two and Three Dimensions

TL;DR

This paper introduces a broad class of exactly solvable non-central potentials in two and three dimensions, extended rationally and involving exceptional orthogonal polynomials, with explicit eigenvalues and eigenfunctions.

Contribution

It constructs new rationally extended non-central potentials in 2D and 3D, including PT-symmetric complex cases, with explicit solutions and polynomial eigenfunctions.

Findings

Explicit energy eigenvalues and eigenfunctions derived.

Wavefunctions related to exceptional orthogonal polynomials.

Extended potentials include real and PT-symmetric complex cases.

Abstract

We start from a seven parameters (six continuous and one discrete) family of non-central exactly solvable potential in three dimensions and construct a wide class of ten parameters (six continuous and four discrete) family of rationally extended exactly solvable non-central real as well as PT symmetric complex potentials. The energy eigenvalues and the eigenfunctions of these extended non-central potentials are obtained explicitly and it is shown that the wave eigenfunctions of these po- tentials are either associated with the exceptional orthogonal polynomials (EOPs) or some type of new polynomials which can be further re-expressed in terms of the corresponding classical orthogonal polynomials. Similarly, we also construct a wide class of rationally extended exactly solvable non-central real as well as complex PT-invariant potentials in two dimensions.