Relativistic Wave Equation for a Quantum Particle With Potential Energy

Abstract

A new relativistic wave equation is derived for a quantum particle which moves in a potential. The relativistic equation of energy is reconsidered with the potential energy term. The energy-momentum relation is obtained for this case. The related differential equation is derived by taking into account a wave function in terms of a plane wave. It is shown that the new equation directly reduces to the Schrodinger equation of a particle, moving in a potential in the non-relativistic limit. The wave equation is applied to the interaction of wave function with a potential barrier.