Construction of Exactly Solvable Potentials from Romanovski Polynomials

Abstract

We apply Extended transformation method to construct exactly solvable potentials of stationary state Schrodinger equation in any arbitrary dimensional Euclidean space. The normalized wave functions of the constructed potentials are obtained in terms of Romanovski polynomials. We show that there are six choices of coordinate transformation each leading to a potential for which Schrodinger equation is exactly solvable in terms of Romanovski polynomials. With analytical calculations we report that out of these six potentials only two are independent.