Mathematical Physics


On the Stationary Orbits of a Hydrogen-Like Atom

Authors: Vu B Ho

In this work we discuss the possibility of combining the Coulomb potential with the Yukawa’s potential to form a mixed potential and then investigate whether this combination can be used to explain why the electron does not radiate when it manifests in the form of circular motions around the nucleus. We show that the mixed Coulomb-Yukawa potential can yield stationary orbits with zero net force, therefore if the electron moves around the nucleus in these orbits it will not radiate according to classical electrodynamics. We also show that in these stationary orbits, the kinetic energy of the electron is converted into potential energy, therefore the radiation process of a hydrogen-like atom does not related to the transition of the electron as a classical particle between the energy levels. The radial distribution functions of the wave equation determine the energy density rather than the electron density at a distance r along a given direction from the nucleus. It is shown in the appendix that the mixed potential used in this work can be derived from Einstein’s general theory of relativity by choosing a suitable energy-momentum tensor. Even though such derivation is not essential in our discussions, it shows that there is a possible connection between general relativity and quantum physics at the quantum level.

Comments: 10 Pages.

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[v1] 2017-08-17 01:50:44

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