Confined Dirac fermions in a constant magnetic field
- Theoretical Physics Group, Faculty of Sciences, Chouaieb Doukkali University, Ibn Maachou Road, P.O. Box 20, 24000 El Jadida (Morocco)
- Saudi Center for Theoretical Physics, Dhahran 31261 (Saudi Arabia)
- Department of Physics, King Fahd University of Petroleum and Minerals, Dhahran 31261 (Saudi Arabia)
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.
- OSTI ID:
- 21313203
- Journal Information:
- Physical Review. A, Vol. 80, Issue 1; Other Information: DOI: 10.1103/PhysRevA.80.012109; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
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