Kinetic energy based relativistic wave equation

Abstract

The Schrodinger equation is based on a Hamiltonian, which is the sum of kinetic and potential energies. The energy term, in the relativistic energy-momentum relation, is divided into its kinetic and rest energy components according to the Hamiltonian of the Schrodinger equation. The differential equation is obtained by using the plane wave representation. It is found that the derived form of the Klein-Gordon equation is more similar to the Schrodinger equation than the classical one. Non-relativistic limit is also studied.