Scalar potentials in the Dirac equation

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Abstract
The Dirac equation for motion in a central potential is generalized to include scalar potentials proportional to r and to r−1. It is solved by analytic methods. The linear dependence upon radius leads to spectra similar to that of the harmonic oscillator except that the approximately constant level distance applies to E2 instead of E. A large negative term in the rest mass displaces the equilibrium point of the oscillator to a large radius.

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