  The recently introduced reconciliation of the theories of special relativity
and wave mechanics implies that the mass-energy equivalence principle must be
expressed mathematically as H = mv^2, where H is the total energy of a
particle, m is its relativistic mass, and v is its velocity; not H = mc^2 as
was widely believed. In this paper, the equation H = mv^2 will be used to
calculate the energy levels in the spectrum of the hydrogen atom. It is
demonstrated that the well-known Sommerfeld-Dirac formula is still obtained,
but without the constant term m_0 c^2 that was originally present in the
formula.
