Spectral Comparison Theorem for the Dirac Equation

Details Spectral Comparison Theorem for the Dirac Equation Spectral Comparison Theorem for the Dirac Equation

1999-06-14

arxiv.org/abs/quant-ph/9906042v1

Phys.Rev.Lett. 83 (1999) 468-471

Physics

Quantum Physics

9 pages. To appear in PRL

Scientific paper

10.1103/PhysRevLett.83.468

We consider a single particle which is bound by a central potential and obeys the Dirac equation. We compare two cases 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.

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