Klein-Gordon equation particles in exponential-type molecule potentials and its thermodynamic properties in D- dimensions

TL;DR

This paper solves the Klein-Gordon and Schrödinger equations with a five-parameter exponential potential using the Nikiforov-Uvarov method, and explores the thermodynamic properties of particles in D-dimensional space.

Contribution

It introduces an approximate solution approach for the Klein-Gordon equation with a complex potential and analyzes thermodynamic properties in non-relativistic limits.

Findings

Derived energy eigenvalues and wave functions for the potential.

Calculated thermodynamic quantities like mean energy, free energy, and specific heat.

Discussed special cases of the potential.

Abstract

In this paper we use the Nikiforv-Uvarov method to obtain the approximate solutions of the Klein-Gordon equation with deformed five parameter exponential type potential (DFPEP) model. We also obtain the solutions of the Schr\"odinger equation in the presence of the DFPEP in the non-relativistic limits. In addition, we calculate in the nonrelativistic limits the thermodynamics properties such as vibrational mean energy U, free energy F and the specific heat capacity C . Special cases of the potential are also discussed.