  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 $c_{h}\rightarrow 0$, the energy spectrum and the corresponding wave
functions for the radial Morse potential are recovered.
