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

Abstract

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.

19 pages, 1 figure

References in corpus (3)

• Any $l$-state solutions of the Hulthén potential by the asymptotic iteration method
• Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
• Approximate l-state solutions of the D-dimensional Schrodinger equation for Manning-Rosen potential

Cited by in corpus (2)

• Exact Klein-Gordon equation with spatially-dependent masses for unequal scalar-vector Coulomb-like potentials
• Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials