Eigensolutions and thermodynamic properties of deformed and modified Morse potential model

T A Akanbi,O Y Oludoun,C A Onate

doi:10.1063/5.0042099

Abstract

A four parameter exponential-type potential known as the deformed and modified Morse potential model was proposed. The solution of the one-dimensional radial Schrӧdinger equation was obtained in the presence of the proposed potential for an arbitrary ℓ-state using a parametric Nikiforov–Uvarov method. The energy equation was used to obtain the eigenvalues for the cesium molecule and tin carbide for various states. The effects of the deformed parameter on the eigenvalues were studied. The result for the Morse potential was obtained by fixing the deformed parameter to zero. Finally, the thermal properties of the proposed potential and the Morse potential were studied in detail. The result obtained revealed that the behavior of the energy eigenvalue for the deformed and modified Morse potential with the deformed parameter (b) equals one, is same as the behavior of the energy eigenvalue for the actual Morse potential.

Highlights

Since the introduction of quantum mechanics, there have been continuous studies on the Schrödinger equation with the exactly solvable exponential-type potential models
In the works of Zhang et al.1 and Jia et al.,3 the improved Manning–Rosen potential known as the Deng–Fan potential or generalized Morse potential has been used to calculate the rotational transition frequencies of hydrogen fluoride (HF)
Motivated by the interest and usefulness of the exponential-type potential model, this study investigates a deformed and modified Morse potential model using the elegant parametric Nikiforov–Uvarov method

Summary

INTRODUCTION

Since the introduction of quantum mechanics, there have been continuous studies on the Schrödinger equation with the exactly solvable exponential-type potential models. The actual Manning–Rosen potential gives an excellent description of the interaction between the two atoms in diatomic molecules and describes the interaction close to the surface This potential has been reported extensively by different authors in terms of bound states and thermodynamic properties.. In order to completely describe the different molecules with the various exponential-type potential models, Jia et al., modified some already existing exponential-type potentials by including some spectroscopic parameters that fit the experimental data for various molecules These modified potential models have recently been studied, and the results were compared with the experimental values. The Rydberg–Klein–Rees (RKR) of the cesium dimer was calculated by Hu et al. with the deformed four parameter exponentialtype potential model. The solutions of the radial Schrödinger equation with the deformed and modified Morse potential are obtained. To obtain the solutions of the radial equation in Eq (2) using the Nikiforov–Uvarov method, Eqs. (3) and (4) are first substituted into Eq (2) to obtain [

Bound state solutions via the parametric Nikiforov–Uvarov method

THE DEFORMED AND MODIFIED MORSE POTENTIAL AND THERMODYNAMIC PROPERTIES

AND DISCUSSION

CONCLUSION