Abstract
We obtain exact solution of the Dirac equation for a charged particle with position-dependent mass in the Coulomb field. The effective mass of the spinor has a relativistic component which is proportional to the square of the Compton wavelength and varies as 1/ r. It is suggested that this model could be used as a tool in the renormalization of ultraviolet divergences in field theory. The discrete energy spectrum and spinor wave-function are obtained explicitly.
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