New bound and scattering state solutions of the Manning–Rosen potential with the centrifugal term

Abstract

We proposed a new approximate scheme for a centrifugal term. Using new approximate formula for 1/r2, we obtained the bound state and scattering state solutions of the Manning–Rosen potential with centrifugal terms. All approximate analytical formulae of energy eigenvalues, normalized wavefunctions and scattering phase shifts are presented. In addition, we also suggested another much better approximate formula to 1/r2 for bound states. All data calculated by the above approximate analytical formulae are compared with those obtained by using the numerical integration method in the bound state and scattering state cases. Furthermore, the complete s-wave scattering state solutions for the Manning–Rosen potential are also naturally derived.