The Rotation-Vibration Spectrum of Diatomic Molecules with the Tietz-Hua Rotating oscillator

TL;DR

This paper derives exact analytical solutions for the vibrational energy levels of diatomic molecules modeled by the Tietz-Hua potential using the Nikiforov-Uvarov method, providing closed-form eigenvalues and eigenfunctions.

Contribution

It presents the first exact analytical solutions for the Schrödinger equation with the Tietz-Hua potential for diatomic molecules.

Findings

Closed-form energy eigenvalues obtained

Eigenfunctions expressed analytically

Numerical results for specific molecules provided

Abstract

The Tietz-Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov-Uvarov (NU) method, we have obtained the exact analytical s-wave solutions of the radial Schr\"odinger equation (SE) for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented.