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

Abstract

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 ) ln λ < 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.