Path integral solutions for Klein-Gordon particle with position-dependent mass in deformed Hulthén potential

Abstract

The Green's function for a Klein-Gordon particle with position-dependent mass under the action of vector plus scalar q-deformed Hulthén potentials is evaluated by exact path integration. From the singularities of the latter Green's function, the bound states are extracted. For , 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. Particular cases of these potentials are also discussed briefly and it is found that the obtained results are in good agreement with those obtained in the literature.