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Title: Confined Dirac fermions in a constant magnetic field

Abstract

We obtain an exact solution of the Dirac equation in (2+1) dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of positive- and negative-energy solutions, each of which splits into two disconnected subspaces depending on the sign of an azimuthal quantum number k=0,{+-}1,{+-}2,... and whether the cyclotron frequency is larger or smaller than the oscillator frequency. The spinor wave function is written in terms of the associated Laguerre polynomials. For negative k, the relativistic energy spectrum is infinitely degenerate due to the fact that it is independent of k. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the relativistic quantum Hall effect in a confining potential.

Authors:
 [1];  [2];  [3]
  1. Theoretical Physics Group, Faculty of Sciences, Chouaieb Doukkali University, Ibn Maachou Road, P.O. Box 20, 24000 El Jadida (Morocco)
  2. Saudi Center for Theoretical Physics, Dhahran 31261 (Saudi Arabia)
  3. Department of Physics, King Fahd University of Petroleum and Minerals, Dhahran 31261 (Saudi Arabia)
Publication Date:
OSTI Identifier:
21313203
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 80; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.80.012109; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; COUPLING; CYCLOTRON FREQUENCY; DIRAC EQUATION; ENERGY SPECTRA; EXACT SOLUTIONS; FERMIONS; HALL EFFECT; LAGUERRE POLYNOMIALS; MAGNETIC FIELDS; OSCILLATORS; POTENTIALS; QUANTUM MECHANICS; RELATIVISTIC RANGE; TWO-DIMENSIONAL CALCULATIONS; WAVE FUNCTIONS

Citation Formats

Jellal, Ahmed, Alhaidari, Abdulaziz D., and Bahlouli, Hocine. Confined Dirac fermions in a constant magnetic field. United States: N. p., 2009. Web. doi:10.1103/PHYSREVA.80.012109.
Jellal, Ahmed, Alhaidari, Abdulaziz D., & Bahlouli, Hocine. Confined Dirac fermions in a constant magnetic field. United States. doi:10.1103/PHYSREVA.80.012109.
Jellal, Ahmed, Alhaidari, Abdulaziz D., and Bahlouli, Hocine. Wed . "Confined Dirac fermions in a constant magnetic field". United States. doi:10.1103/PHYSREVA.80.012109.
@article{osti_21313203,
title = {Confined Dirac fermions in a constant magnetic field},
author = {Jellal, Ahmed and Alhaidari, Abdulaziz D. and Bahlouli, Hocine},
abstractNote = {We obtain an exact solution of the Dirac equation in (2+1) dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of positive- and negative-energy solutions, each of which splits into two disconnected subspaces depending on the sign of an azimuthal quantum number k=0,{+-}1,{+-}2,... and whether the cyclotron frequency is larger or smaller than the oscillator frequency. The spinor wave function is written in terms of the associated Laguerre polynomials. For negative k, the relativistic energy spectrum is infinitely degenerate due to the fact that it is independent of k. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the relativistic quantum Hall effect in a confining potential.},
doi = {10.1103/PHYSREVA.80.012109},
journal = {Physical Review. A},
number = 1,
volume = 80,
place = {United States},
year = {Wed Jul 15 00:00:00 EDT 2009},
month = {Wed Jul 15 00:00:00 EDT 2009}
}
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