Path integral solution for a deformed radial Rosen-Morse potential

Abstract

An exact path integral treatment of a particle in a deformed radial Rosen-Morse potential is presented. For this problem with the Dirichlet boundary conditions, the Green's function is constructed in a closed form by adding to V_{q}(r) a {\delta}-function perturbation and making its strength infinitely repulsive. A transcendental equation for the energy levels E_{n_{r}} and the wave functions of the bound states can then be deduced.