Equivalence of the empirical shifted Deng-Fan oscillator potential for diatomic molecules

TL;DR

This paper derives analytical solutions for the bound states of the shifted Deng-Fan oscillator potential in diatomic molecules using the NU method, providing results consistent with Morse potential calculations.

Contribution

It introduces a closed-form solution for the Schrödinger equation with the shifted Deng-Fan potential, including energy levels and wave functions, using Pekeris approximation and NU method.

Findings

Energy eigenvalues match previous Morse potential results

Analytical wave functions are obtained in closed form

Ro-vibrational levels are accurately calculated for diatomic molecules

Abstract

We obtain the bound-state solutions of the radial Schr\"odinger equation (SE) with the shifted Deng-Fan (sDF) oscillator potential in the frame of the Nikiforov-Uvarov (NU) method and employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding wave functions are obtained in closed form for arbitrary -state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.