Spectral Comparison Theorem for the Dirac Equation
Quantum Physics
2009-10-31 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.quant-ph/9906042,
title = {Spectral Comparison Theorem for the Dirac Equation},
author = {Richard L. Hall},
journal= {arXiv preprint arXiv:quant-ph/9906042},
year = {2009}
}
Comments
9 pages. To appear in PRL