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.

A rigorous evaluation of the path integral for Green's function associated with a four-parameter potential for a diatomic molecule is presented. A closed form of Green's function is obtained for different shapes of this potential. When the deformation parameter is Ͻ0 or 0ϽϽ1, it is found that the quantization conditions are transcendental equations that require a numerical solution. For ജ1 and r ͔͑1/͒ln , ϱ͓, the energy spectrum and the normalized wave functions of the bound states are derived. Particular cases of this potential which appear in the literature are also briefly discussed.

No abstract

No abstract

The approximate bound state solutions of Schrödinger equation with linear combination of a q-deformed Hulthén potential plus screened Kratzer potential were obtained with the help of appropriate approximation to evaluate the centrifugal term. The Feynman path integral approach was used to obtain the analytical solutions. The energy spectrum and the normalized wave functions of the bound states are derived from the poles of the Green’s function and its residues. Particular cases of these potentials are also discussed briefly and it is found that obtained results are in good agreement with those obtained in the literature.