Abstract

Einstein’s energy-momentum relationship holds for isolated systems in free space. However, this relationship cannot be applied to an electron in a hydrogen atom where potential energy exists. Thus, the author has previously derived an energy-momentum relationship applicable to an electron in a hydrogen atom using three methods. When the formula for this relationship is solved, the hydrogen atom has energy levels that can take negative values, even when described on an absolute scale. When an electron transitions to this negative energy level, it is not enough even if it releases all of the rest mass energy m_ec². Thus, the author pointed out that the electron has unknown photon energy in addition to its rest mass energy. The author predicted—but was unable to prove—the existence of this unknown energy. In this paper, the energy-momentum relationship applicable to an electron in a hydrogen atom is derived using two methods different from those used previously. The paper also elucidates the latent photon energy of the electron, and the existence of negative energy which cancels that out.

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