Effect of a relativistic correction to the Coulomb potential on the energy levels of hydrogen atom
Abstract
Based on classical electrodynamics, it is argued that the Coulomb potential (which is strictly valid for two point charges at rest), commonly used in the study of energy levels of hydrogen atom is not the correct one, because the electron in the hydrogen atom moves with relativistic speeds with respect to the nucleus. Retardation effect has to be considered in accordance with LiénardWiechert (or retarded) potential of a moving charge or the relativistic electrodynamics. However, such a consideration introduces a correction to the Coulomb potential, whose quantum mechanical expectation value is estimated at $E_{ret} =  \frac{mc^2\alpha ^4}{2n^3(l+1/2)}$, which is of the same order as the fine structure of hydrogen atom and hence added to the standard energy eigenvalue values of Hatom. This correction lifts the $l$degeneracy in the spectra of Hatom and hence modifies the standard result. The result disturbs the existing agreement between the theory and experiments on Hatom and hence requires further theoretical and experimental reexamination. The implications of this result for the Keplerproblem in general is also discussed in the context of Heaviside's gravity, which seems to offer an alternative explanation for the nonNewtonian perihelion advance of Mercury without invoking the spacetime curvature formalism of Einstein's general theory of relativity.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 DOI:
 10.48550/arXiv.1201.1619
 arXiv:
 arXiv:1201.1619
 Bibcode:
 2012arXiv1201.1619B
 Keywords:

 Physics  General Physics
 EPrint:
 6 pages, 1 figure