The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's function associated with different shapes of the potentials. For q ≤ −1, and 1 2α ln |q| < r < +∞, the energy equation and the corresponding wave functions are deduced for the l states using an appropriate approximation to the centrifugal potential term. When −1 < q < 0 or q > 0, it is shown that the quantization conditions for the bound state energy levels En r are transcendental equations which can be solved numerically. Three special cases such as the standard radial Manning-Rosen potential (|q| = 1), the standard radial Rosen-Morse potential (V2 → −V2, q = 1) and the radial Eckart potential (V1 → −V1, q = 1) are also briefly discussed.

An exact path integral treatment of a particle in a deformed radial Rosen-Morse potential is presented. For this problem with the Dirichlet boundary conditions, the Green's function is constructed in a closed form by adding to Vq(r) a δ−function perturbation and making its strength infinitely repulsive. A transcendental equation for the energy levels En r and the wave functions of the bound states can then be deduced.

In this work, the bound state problem of some diatomic molecules in the Tietz-Wei potential with varying shapes is correctly solved by means of path integrals. Explicit path integration leads to the radial Green's function in closed form for three different shapes of this potential. In each case, the energy equation and the wave functions are obtained from the poles of the radial Green's function and their residues, respectively. Our results prove the importance the optimization parameter c h in the study of this potential which has been completely ignored by the authors of the papers cited below. In the limit c h → 0, the energy spectrum and the corresponding wave functions for the radial Morse potential are recovered.

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