Path integral solution for a deformed radial Rosen-Morse potential

TL;DR

This paper derives an exact path integral solution for a particle in a deformed radial Rosen-Morse potential, providing explicit Green's functions and energy spectra for bound states.

Contribution

It introduces a novel path integral approach to solve the deformed radial Rosen-Morse potential with closed-form Green's functions and energy equations.

Findings

Closed-form Green's function for the potential

Transcendental equations for energy levels

Explicit bound state wave functions

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.