Eigensolutions and Thermodynamic Properties of Kratzer plus generalized Morse Potential

TL;DR

This paper derives exact solutions for the Schrödinger equation with Kratzer plus generalized Morse potential, and analyzes thermodynamic properties of lithium hydride molecules, confirming results with existing literature.

Contribution

It provides closed-form energy eigenvalues and wave functions for the combined potential, and applies these to study thermodynamics of diatomic molecules.

Findings

Thermodynamic properties match existing literature.

Wave functions and probability densities are computed accurately.

Energy eigenvalues are obtained analytically.

Abstract

In this study, we apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrodinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM). The energy eigen equation and the corresponding normalised wave function were obtained in closed form. The resulting energy eigen equation were use to study partition function and other thermodynamic properties such as vibrational mean energy, vibrational specific heat capacity, vibrational mean free energy and vibrational entropy for the proposed potential as applied to lithium hydride diatomic molecule. The thermodynamic plots obtained were in excellent agreement to work of existing literatures. The wave function and probability density plots for the diatomic molecules were obtained through a well designed and implemented maple programme.