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

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

2009-01-07

arxiv.org/abs/0901.0801v1

European Physical Journal A 39 (2009) 307-314.

Physics

Quantum Physics

19 pages, 1 figure

Scientific paper

10.1140/epja/i2008-10715-2

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.

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