Semi-inverse variational approach to solve the Klein-Gordon equation for harmonic- and perturbed Coulomb potentials

Abstract

The events observable at the atomic scale cannot be adequately explained by classical physics, hence a new conceptual framework for physics must be developed. "Quantum mechanics" is the name given to this new theory of the physical cosmos. The basic formula of relativistic quantum mechanics is the problem of Klein-Gordon. In relativistic quantum physics, the wave function is crucial since it contains all the data describing a quantum system, in relativity quantum physics, they are crucial. How to solve Klein Gordon's equation has been the topic of intense debate in recent years. To determine the system's spectrum using numerous potentials and methodologies. To obtain the Klein-Gordon issues solution Through determining the harmonic and perturbed Coulomb potentials' energies, The recent study employed an entirely distinct methodology. using the Semi-Inverse Variational Technique to aid in the process, we were able to identify the eigen energies for Harmonic- and Perturbed Coulomb Potentials for a variety of quantum numbers. A further benefit of the technique was that it enabled us to obtain the wave eigenfunctions for various potentials, demonstrating the viability of this approach. We are excited to deal with additional challenges in our upcoming works, the first being the use of nonlinear potentials to solve the Dirac equation due to the effectiveness of this approach.