Spectral comparison theorem for the N-dimensional Dirac equation

Journal Article · Sat Oct 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.044102· OSTI ID:20718820

Gang, Chen ^[1]

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1. Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000 (China) and Institute of Theoretical Physics, Shanxi University, Taiyuan 030006 (China)

This Brief Report is concerned with the discrete spectrum of the N-dimensional Dirac equation. Through the spectral comparison theory demonstrated here the discrete spectrum is obtained approximately without actually having to solve the N-dimensional Dirac equation as well as the lower-dimensional cases. This comparison theorem states that if two time-independent attractive potentials are different such that V{sub a} < V{sub b}, the corresponding energy spectrum satisfies the inequality E{sub a} < E{sub b}. As an illustrative example, the Hellmann potential is considered with the aid of the comparison theorem and potential envelope method.

• OSTI ID: 20718820
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
COMPARATIVE EVALUATIONS
DIRAC EQUATION
ENERGY LEVELS
ENERGY SPECTRA
POTENTIALS
QUANTUM MECHANICS