Exact path integral treatment of a diatomic molecule potential

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 λ is λ<0 or 0<λ<1, it is found that the quantization conditions are transcendental equations that require a numerical solution. For λ≥1 and r set-membership sign](1/η)ln λ,∞[, 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