Path integral discussion of the improved Tietz potential 1

TL;DR

This paper applies the path integral formalism to analyze an improved Tietz potential, deriving the Green's function and energy spectrum for diatomic molecules, including special cases like the Morse potential.

Contribution

It provides a rigorous path integral approach to the improved Tietz potential, deriving explicit Green's functions and energy spectra, including numerical solutions for certain parameter regimes.

Findings

Closed-form radial Green's function constructed.

Energy spectrum derived for different potential shapes.

Numerical solutions required for certain deformation parameters.

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.