Eigensolutions of the N-dimensional Schr\"odinger equation interacting with Varshni-Hulth\'en potential model

Analytical solutions of the N-dimensional Schr\"odinger equation for the newly proposed Varshni-Hulth\'en potential are obtained within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier. The numerical energy eigenvalues and the corresponding normalized eigenfunctions are obtained in terms of Jacobi polynomials. Special cases of the potential are equally studied and their numerical energy eigenvalues are in agreement with those obtained previously with other methods. However, the behavior of the energy for the ground state and several excited states is illustrated graphically.