Whether or not the Maxwell theory works on the atomic level

Abstract

In this paper, we have studied the Maxwell radiation from the electron orbiting the nucleus in an atom such as hydrogen atom. The orbiting electron is thought as two oscillating dipoles: one on [Formula: see text]-axis and the other on [Formula: see text]-axis with the same frequency. We have derived the electromagnetic wave and calculated powers of the radiation from these two oscillating dipoles, and then determined the time period it takes for the electron to change its energy levels from [Formula: see text] to [Formula: see text] due to the Maxwell radiation. Compared the time period due to the Maxwell radiation with the time period from the uncertainty principle, it is found that the two time periods are different from each other by about nine orders of magnitude. So, we are led to believe that the Maxwell theory could not be used in the quantum photo emission by the electron in an atom. Thus, we suggest that the quantum photo emission by the electron in an atom may be photon tunneling from the electron [Formula: see text] in an atom.