Eigenspectra and Statistical Properties of the Klein-Gordon Equation with Cornell Potential: Unequal Mixings of Scalar and Time-Like Vector Potentials

TL;DR

This paper solves the Klein-Gordon equation with Cornell potentials to find bound state energies and statistical properties, providing insights relevant to relativistic heavy quarkonium systems in particle physics.

Contribution

It introduces a novel solution method for the Klein-Gordon equation with unequal scalar and vector Cornell potentials and analyzes their statistical properties.

Findings

Calculated bound state energy eigenvalues for heavy quarkonium.

Analyzed the statistical properties of the system.

Provided insights into relativistic particle behavior.

Abstract

The D-dimensional Klein-Gordon (KG) wave equation with unequal scalar and time-like vector Cornell interactions is solved by the Laplace transform method. In fact, we obtained the bound state energy eigenvalues of the spinless relativistic heavy quarkonium systems under such potentials. Further, the stationary states are calculated due to the good behavior of wave functions at the origin and at infinity. The statistical properties of this model are also investigated. Our results are found to be of great importance in particle physics.