Spectral Comparison Theorem for the Dirac Equation

Journal Article · Thu Jul 01 04:00:00 EDT 1999 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.83.468· OSTI ID:355464

Hall, R L ^[1]

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1. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, H3G 1M8 (CANADA)

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 V{sub a}{lt}V{sub b}, 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 E{sub a}{lt}E{sub b}. As an illustration, this general relativistic comparison theorem is applied to approximate the Dirac spectrum generated by a screened-Coulomb potential. {copyright} {ital 1999} {ital The American Physical Society}

• OSTI ID: 355464
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 3 Vol. 83; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
COULOMB FIELD
DIRAC EQUATION
EIGENVALUES
ENERGY SPECTRA
HAMILTONIANS
POTENTIAL ENERGY
RELATIVISTIC RANGE
WAVE FUNCTIONS