Analytical solutions of the Schrödinger equation with the Manning-Rosen potential plus a Ring-Shaped like potential

The analytical solution of the Schr\"{o}dinger equation for the Manning-Rosen potential plus a ring-shaped like potential is obtained by applying the Nikiforov-Uvarov method by using the improved approximation scheme to the centrifugal potential for arbitrary \(l\) states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary \(l\) states.