Unified path integral treatment for generalized Hulthén and Woods-Saxon potentials

A rigorous path integral discussion of the s states for a diatomic molecule potential with varying shape, which generalizes the Hulthén and the Woods-Saxon potentials, is presented. A closed form of the Green’s function is obtained for different shapes of this potential. For λ ? 1 and (1/η)lnλ<r<∞, the energy spectrum and the normalized wave functions of the bound states are derived. When the deformation parameter λ is 0 < λ < 1 or λ < 0, it is found that the quantization conditions are transcendental equations that require numerical solutions. The special cases corresponding to a screened potential (λ = 1), the deformed Woods-Saxon potential (λ = q e^ηR), and the Morse potential (λ = 0) are likewise treated.