Path integral discussion of the improved Tietz potential 1

An improved form of the Tietz potential for diatomic molecules is \ discussed in detail within the path integral formalism. The radial Green's function is rigorously constructed in a closed form for different shapes of this potential. For $\left\vert q\right\vert \leq 1,$ and $\frac{1}{2\alpha } \ln \left\vert q\right\vert <r<+\infty$, the energy spectrum and the normalized wave functions of the bound states are derived for the $l$ waves. When the deformation parameter $q$ is $0<\left\vert q\right\vert <1$ or $q>0$% , it is found that the quantization conditions are transcendental equations that requires numerical solutions. In the limit $q\rightarrow 0$, the energy spectrum and the corresponding wave functions for the radial Morse potential are recovered.