  We present a new approximation scheme for the centrifugal term to solve the
Schrodinger equation with the Hulthen potential for any arbitrary l state by
means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound state
energy eigenvalues and the normalized corresponding eigenfunctions expressed in
terms of the Jacobi polynomials or hypergeometric functions for a particle
exposed to this potential field. Our numerical results of the energy
eigenvalues are found to be in high agreement with those results obtained by
using the program based on a numerical integration procedure. The s-wave (l=0)
analytic solution for the binding energies and eigenfunctions of a particle are
also calculated. The physical meaning of the approximate analytical solution is
discussed. The present approximation scheme is systematic and accurate.
