Spectral Comparison Theorem for the Dirac Equation

We consider a single particle which is bound by a central potential and obeys the Dirac equation. We compare two cases, a and b, in which the masses are the same but Va<Vb, where V is the time component of a vector potential. We prove generally that for each discrete eigenvalue E whose corresponding (large and small) radial wave functions have no nodes, it necessarily follows that Ea<Eb. As an illustration, this general relativistic comparison theorem is applied to approximate the Dirac spectrum generated by a screened-Coulomb potential. copyright 1999 The American Physical Society