Bound States for a Klein–Gordon Particle in Vector Plus Scalar Generalized Hulthén Potentials in D Dimensions

Abstract

The Green’s function associated with a Klein–Gordon particle moving in a D-dimensional space under the action of vector plus scalar q-deformed Hulthen potentials is constructed by path integration for \({q \geq 1}\) and \({\frac{1}{\alpha} \ln q < r < \infty}\). An appropriate approximation of the centrifugal potential term and the technique of space-time transformation are used to reduce the path integral for the generalized Hulthen potentials into a path integral for q-deformed Rosen–Morse potential. Explicit path integration leads to the radial Green’s function for any l state in closed form. The energy spectrum and the correctly normalized wave functions, for a state of orbital quantum number \({l \geq 0}\), are obtained. Eventually, the vector q-deformed Hulthen potential and the Coulomb potentials in D dimensions are considered as special cases.