Path integral discussion of the improved Tietz potential 1
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.12310
 Bibcode:
 2019arXiv191112310K
 Keywords:

 Quantum Physics
 EPrint:
 17 pages