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 Hulthen 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)lnλtranscendental equations that require numerical solutions. The special cases corresponding to a screened potential (λ = 1), the deformed Woods–Saxon potential (λ = q eηR), and the Morse potential (λ = 0) are likewise treated.