Analytical solutions of the $D$-dimensional Schrödinger equation with the Woods-Saxon potential for arbitrary $l$ state

In this work, the analytical solution of the hyper-radial Schrödinger equation for the spherical Woods-Saxon potential in D dimensions is presented. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary $l$ states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of $n$ and $l$ quantum numbers.