For the hydrogen atom, a single relativistic wave equation in Whittaker form was derived which yields the energy level spectrum, the same as that given by the Dirac (coupled system of) equations. Unlike the usual treatments of the Dirac equation, the solutions presented here do not diverge at infinity, in fact they approach zero. Also, for Z<119, it is shown that the usual energy levels follow; however, for 119<Z<137 the spectrum depends on a free parameter.

Topics
Partial differential equations, Chemical elements, Dirac equation, Relativistic wave equations
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