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
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.
PACS: 03.65.Ge Solutions of wave equations: bound states – / 12.39.Jh Nonrelativistic quark model –
© SIF, Springer-Verlag Berlin Heidelberg, 2009
