The analytical resolution of Klein–Gordon equation with vector and scalar for Coulomb plus Yukawa potentials

Similar to how general relativity emerged, quantum mechanics resulted from experimental observations that made us radically rethink our previous assumptions. Scientists who study atoms need to solve these three equations. They are for a system with N electrons affected by the nucleus’s attractive Coulomb force and the repulsive force between each pair of electrons and other potentials. While general relativity has upended our large-scale conception of the universe, quantum mechanics calls into question all our intuition regarding particle physics. The Klein–Gordon (KG) resolution helps determine some physical systems and their properties by finding their bound states and eigenfunctions. These are resolved using analytical and numerical methods, as well as Coulomb and Yukawa potentials. In order to extract some of the first eigenvalues of the quantum mechanical system, we applied the Nikiforov–Uvarov (NU) method to the KG equation. The findings are significant for understanding nuclear charge radius, spin, nuclear diffusion and other topics in numerous theoretical physics and quantum chemistry fields because they are more generic and helpful.