Classical Theory of Radiation Solutions for the Coulomb Field

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Abstract
Eliezer has contended that the Dirac equations for the motion of a particle in a Coulomb field, when the radiative reaction is included, do not have physically realizable solutions. The problem is reinvestigated and Eliezer's conclusion proved false. Two-dimensional solutions (spirals) are found, which can be described with the exclusive use of integrable functions. One-dimensional solutions (radial trajectories) are found for both a repulsive and an attractive pole. The radial solutions involve distributions (in the sense of Schwartz). A consequence of the solutions is the emission of a strong pulse of radiation when a particle hits an attractive pole or when it leaves a respulsive one.

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