L-states of the Manning–Rosen potential with an improved approximate scheme and Feynman path integral formalism

Abstract

A new analytical expression for the energy eigenvalues of the Manning–Rosen potential for l-states, based on the path integral formalism, is derived by an improved approximation to the centrifugal term of the potential, in the framework of the Duru–Keinert method. Nonlinear space–time transformations in the radial path integral are applied. A transformation formula is derived that relates the original path integral to the Green function of a new quantum soluble system. The energy spectrum and the normalized eigenfunctions are both obtained for the application of this technique to the Manning–Rosen potential. Our results are in very good agreement with those found by using numerical and other approximation methods. Our solution applies also to the Hulthén potential.