Research Article | Open Access

# Exact Solutions of the Mass-Dependent Klein-Gordon Equation with the Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential

**Academic Editor:**S. H. Dong

#### Abstract

Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

#### 1. Introduction

The movement of a particle with harmonic oscillations around an equilibrium position creates one of the most fundamental problems of physics. The basic structure of different systems such as vibration of the diatomic molecules, oscillations of atoms in crystal lattices, or nucleons in core is a harmonic oscillator problem [1]. Further, the quantum theory of electromagnetic fields is closely related to the examples of the harmonic oscillator [2, 3]. When a particle is in a strong potential field, the relativistic effect must be considered. However, in relativistic and nonrelativistic quantum mechanics, many authors have adequately the harmonic oscillator problem [4, 5]. But, it has never been investigated for relativistic particles with position-dependent mass (pdm). Quantum mechanical review of relativistic s