Volume 24: Pages 301-307, 2011 (doi:http://dx.doi.org/10.4006/1.3583810)

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

KoshunSuto ^a

5-24 Oote Town, Isesaki City 372-0048, Japan

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.

L'équation d'Einstein reliant l'énergie et la quantité de mouvement, qui est représentative de la théorie de la relativité restreinte, est valide dans un système isolé de l'espace. Cependant, il est considéré en terme général que le comportement des électrons dans un atome est mieux décrit par les équations comme celle de Dirac, qui appartiennent au domaine de la physique quantique. Dans cet article, nous sommes partis de la question suivante: “Si une équation similaire à celle d'Einstein peut rester vrai pour un atome d'hydrogène, quelle sera alors la forme de cette nouvelle équation?” Ainsi, l'équation induite par ce travail pourrait s'avérer complémentaire à la mécanique quantique.

Keywords: Einstein's Energy-Momentum Relationship, Special Theory of Relativity, Dirac Equation, Rest Mass Energy, Relativistic Energy, Hydrogen Atom, Potential Energy, Total Mechanical Energy

Received: July 14, 2010; Accepted: April 9, 2011; Published Online: May 9, 2011

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