Abstract

In this paper an equation with higher precision than the equation of quantum mechanics is derived as an equation describing the energy levels of the hydrogen atom using only the principal quantum number n. That equation predicts the existence of an n=0 energy level. However, the state where n=0 is not an energy level of the electron comprising the hydrogen atom. The electron in this state forms a pair with a positron, which is the electron's antiparticle. The relativistic energy of the individual particles forming the pair is zero, but their momentum is not zero. The momentums of these particles are equal in magnitude but opposite in direction. By forming a pair, the sum of the momentums of two types of particles becomes zero. It is very significant that even the energy level of the electron pairs which comprise the vacuum have been incorporated into the formula for the energy of the hydrogen atom.

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