Path integral solutions for Klein–Gordon particle in vector plus scalar generalized Hulthén and Woods–Saxon potentials

Abstract

The Green’s function for a Klein–Gordon particle under the action of vector plus scalar deformed Hulthén and Woods–Saxon potentials is evaluated by exact path integration. Explicit path integration leads to the Green’s function for different shapes of the potentials. From the singularities of the latter Green’s function, the bound states are extracted. For q≥1 and (1/α)ln q<r<∞, the analytic expression of the energy spectrum and the normalized wave functions for the l states are obtained within the framework of an approximation to the centrifugal term. When the deformation parameter q is 0<q<1 or q<0, it is found that the quantization conditions are transcendental equations involving the hypergeometric function that require a numerical solution for the s-state energy levels. Particular cases of these potentials are also discussed briefly.