Feynman integral treatment of the Rosen–Morse potential with a centrifugal term approximation

Abstract

In this paper, we present analytic solutions of the Feynman propagator with the Rosen–Morse potential. To this end, an approximation of the centrifugal potential for any l state is used and nonlinear space–time transformations in the radial path integral are applied. A transformation formula that relates the original path integral to the Green function of a new quantum soluble system is derived. Explicit expressions of the bound state energy spectra and the eigenfunctions are obtained and compared to those of Schrödinger formalism. The Eckart potential is also treated as a special case.