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.

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