The recent [Phys. Essays 15,1 (2002)] reconciliation of the theories of special relativity and "wave mechanics implies that the mass-energy equivalence principle must be expressed mathematically as H = [mv.sup.2], where H is the total energy of a particle, m is its relativistic mass, and v is its velocity, not as H = [mc.sup.2], as was widely believed. In this paper the equation H = [mv.sup.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.sub.0][c.sup.2] that was originally present in the formula.
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On the Equation H=mv... and the Fine Structure of the Hydrogen Atom