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

An improved approximation scheme for the centrifugal term and the Hulthen potential