An energy-momentum relationship for a bound electron inside a hydrogen atom

Einstein's energy-momentum relationship, which is representative of the special theory of relativity, holds true in an isolated system in free space, but quantum mechanics as represented by the Dirac equation has been considered the best theory to describe the behavior of electrons possessing potential energy inside atoms. This paper asks the following question: "if a formula similar to Einstein's relationship, which holds true in free space, were to also hold true inside a hydrogen atom, what would such a formula look like?" and then derives this relationship. The newly derived formula of this paper could prove useful as a formula to supplement quantum mechanics. (C) 2011 Physics Essays Publication. [DOI: 10.4006/1.3583810]