Abstract

For a particle at rest in macroscopic space that begins moving when energy is added, the equation for Einstein's energy-momentum relationship represents the relationship between the particle's total energy and momentum, and rest mass energy. When the kinetic energy of the particle increases, so does its total energy. However, things are different when electrons at rest approach the nuclei of hydrogen atoms - protons - thereby creating hydrogen atoms. An electron with rest mass energy will reduce its total energy by emitting photons outside the atom but at the same time will gain kinetic energy. This paper derives the following relationship for an electron inside a hydrogen atom: When establishing the coefficient for the Dirac equation, a relativistic wave equation, Dirac assumed that this equation satisfied the Klein-Gordon equation. However, the Klein-Gordon equation is a quantized equation of Einstein's relationship. Thus, we attempt to discover a coefficient for the Dirac equation which satisfies this quantized relationship as is newly derived in this paper. However, these are not intended to disaffirm the Dirac equation; rather, the equations in this paper with these discovered coefficients are presented as alternative forms of the Dirac equation.