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 $\left|q\right|\le 1,$ and $\frac{1}{2\alpha }\ln \left|q\right|<r<+\infty$, the energy spectrum and the normalized wave functions of the bound states are derived for the $l$ waves. When the deformation parameter $q$ is $0<\left|q\right|<1$ or $q>0$% , it is found that the quantization conditions are transcendental equations that requires numerical solutions. In the limit $q\to 0$, the energy spectrum and the corresponding wave functions for the radial Morse potential are recovered.

17 pages

References in corpus (4)

• A new deformed Schioberg-type potential and ro-vibrational energies for some diatomic molecules
• Approximate relativistic bound state solutions of the Tietz-Hua rotating oscillator for any -state
• Spectroscopic study of some diatomic molecules via the proper quantization rule
• Path integral solution for a Klein-Gordon particle in vector and scalar deformed radial Rosen-Morse-type potentials