Arbitrary l-state solutions of the Feynman propagator for the Rosen-Morse Potential with a centrifugal term approximation

We present analytic solutions of the Feynman propagator with the Rosen-Morse potential. To do that, an approximation of the centrifugal potential is used and nonlinear space-time transformations are applied. A relation between the original path integral and 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 Schrodinger formalism