Limits on Application of the Formula for Potential Energy of a Hydrogen Atom and a Previously Unknown Formula

The author has previously shown that ultra-low energy levels exist among the energy levels of a hydrogen atom, in addition to the energy levels predicted by quantum mechanics. The author has also pointed out that the reduction in rest mass energy of the electron m e c 2 corresponds to potential energy of an electron inside a hydrogen atom. Based on this idea, when an electron that has been taken into the region of a hydrogen atom comes to the point of the classic electron radius r e , its potential energy becomes − m e c 2 , and the electron’s rest mass energy is depleted. Therefore, r e ≤r∞ is the region where the well-known formula for potential energy of an electron is applicable. Rest mass energy is not sufficient for an electron to approach closer than that to the atomic nucleus. Under these conditions, an electron cannot attain ultra-low energy levels. Thus, taking a hint from renormalization theory, the author has predicted that the energy of a stationary electron is actually not m e c 2 , and instead that the electron has a photon energy of 2 m e c 2 and a negative energy specific to the electron of − m e c 2 . When this model is used, it becomes possible for the electron to approach the point r= r e /4 regarded as the radius of the proton. This paper derives a new formula for potential energy of an electron in regions outside the scope of application of the existing formula for potential energy.