Solution of Schrödinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation

Abstract

Exact solutions of the Schrödinger equation for two different potentials are presented by using the extended Nikiforov-Uvarov method. The first one is the inverse square root potential which is a long-range potential and the second one is a combination of Coulomb, linear, and harmonic potentials which is often used to describe quarkonium. Eigenstate solutions are obtained in a systematic way without using any ansatz or transformation. Eigenfunctions for considered potentials are given in terms of biconfluent Heun polynomials.