Complete non-relativistic bound state solutions of the Tietz-Wei potential via the path integral approach

TL;DR

This paper solves the bound state problem of diatomic molecules in the Tietz-Wei potential using path integrals, deriving explicit Green's functions, energy spectra, and wave functions for various potential shapes.

Contribution

It provides a complete non-relativistic solution to the Tietz-Wei potential using path integrals, highlighting the role of the optimization parameter ignored in previous studies.

Findings

Explicit radial Green's functions for three potential shapes

Energy spectra and wave functions derived from Green's function poles

Recovery of Morse potential results in the limit of zero optimization parameter

Abstract

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.