A class of exactly solvable rationally extended non-central potentials in two and three dimensions

Abstract

We start from a seven parameter (six continuous and one discrete) family of non-central exactly solvable potentials 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 potentials are either associated with the exceptional orthogonal polynomials 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.