Generalized improved non-central potential and solution of Schrödinger equation with extended ring-shaped potential via Nikiforov-Uvarov method

Abstract

We propose a generalized improved non-central potential (GINCP) and reconstruct few ring-shaped and double-ring-shaped potentials earlier solved by different researchers. We construct an extended ring-shaped potential (ERSP). Using the Nikiforov-Uvarov (NU) method, we solve the Schrodinger equation with inversely quadratic Coulomb plus ERSP and inversely quadratic harmonic oscillator plus ERSP to obtain eigenvalues and wave functions for these potentials. We also determine eigenvalues for different types of ring-shaped potentials using the obtained eigenvalues. Solutions of the Schrodinger equation with these potentials are applicable to find dynamical properties of physical and chemical quantum mechanical systems.