  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
Li\'{e}nard-Wiechert (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 H-atom. This correction lifts the
$l$-degeneracy in the spectra of H-atom and hence modifies the standard result.
The result disturbs the existing agreement between the theory and experiments
on H-atom and hence requires further theoretical and experimental
re-examination. The implications of this result for the Kepler-problem in
general is also discussed in the context of Heaviside's gravity, which seems to
offer an alternative explanation for the non-Newtonian perihelion advance of
Mercury without invoking the space-time curvature formalism of Einstein's
general theory of relativity.
