The scattering states of the generalized Hulthén potential with an improved new approximate scheme for the centrifugal term

This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrödinger equation for the generalized Hulthén potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the generalized Hulthén potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthén potential and Woods–Saxon potential are also studied briefly