Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potential

A new approximation scheme to the centrifugal term is proposed to obtain the l not equal 0 bound-state solutions of the Schrodinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding normalized wave functions are also found in terms of the Jacobi polynomials. To show the accuracy of the new proposed approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential parameter sigma(0). Our numerical results are of high accuracy like the other numerical results obtained by using program based on a numerical integration procedure for short-range and long-range potentials. The energy bound-state solutions for the s-wave (l = 0) and sigma(0) = 1 cases are given. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei