Eur. Phys. J. A (2009) 39: 307-314
https://doi.org/10.1140/epja/i2008-10715-2

Regular Article - Theoretical Physics

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

Department of Physics, Near East University, Nicosia, North Cyprus, Turkey

Received: 24 November 2008
Revised: 2 January 2009
Accepted: 2 January 2009
Published online: 3 February 2009

Abstract

We present a new approximation scheme for the centrifugal term to solve the Schrödinger equation with the Hulthén 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 = 0analytic 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.