New solutions to the Dirac equation for particles in a magnetic field and a medium

2012 ◽  
Vol 43 (6) ◽  
pp. 727-741 ◽  
Author(s):  
I. A. Balantsev ◽  
A. I. Studenikin ◽  
I. V. Tokarev
Keyword(s):  
Magnetic Field ◽  
Dirac Equation

ON A RESULT CONCERNING THE BEHAVIOR OF A RELATIVISTIC QUANTUM SYSTEM IN THE COSMIC STRING SPACETIME

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1549-1556 ◽  
Author(s):  
V. B. BEZERRA ◽  
GEUSA DE A. MARQUES
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Quantum System ◽  
Relativistic Electron ◽  
Coulomb Potential ◽  
Cosmic String ◽  
Relativistic Quantum

We consider the problem of a relativistic electron in the presence of a Coulomb potential and a magnetic field in the background spacetime corresponding to a cosmic string. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle.

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

CHIRAL ANOMALY IN EUCLIDEAN (2+1)-DIMENSIONAL SPACE AND AN APPLICATION TO THE QUANTUM HALL EFFECT

2008 ◽  
Vol 22 (17) ◽  
pp. 2675-2689 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Magnetic Field ◽  
Dirac Equation ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Zero Mode ◽  
Dimensional Space ◽  
Quantum Hall ◽  
Chiral Anomaly ◽  
Regularization Procedure ◽  
Chiral Transformation

The chiral anomaly in (2+1)-dimensions and its relationship to the zero mode of the Dirac equation in the massless case is studied. Solutions are obtained for the Dirac equation under a vector potential which generates a constant magnetic field. It is shown that there is an anomaly term associated with the corresponding chiral transformation. It can be calculated by using the regularization procedure of Fujikawa. The results are applied to the quantum Hall effect.

POLYNOMIAL SOLUTIONS OF HEUN EQUATION DESCRIBING FERMIONS IN GRAPHENE

2013 ◽  
Vol 27 (32) ◽  
pp. 1350190 ◽  
Author(s):  
MARINA-AURA DARIESCU ◽  
CIPRIAN DARIESCU
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Current Density ◽  
Hermite Polynomials ◽  
Heun Equation ◽  
Conserved Current ◽  
Familiar Form ◽  
The Magnetic Field ◽  
Massless Fermions

The wavefunctions describing the massless fermions evolving in a static magnetic field orthogonal to a radially planar electric field are obtained, as solutions to Dirac equation. In the case of the magnetic field alone, the corresponding HeunB confluent functions turn into the usual Hermite polynomials and the energy spectrum has the familiar form which has been reported for graphene samples. Within a more involved analysis with both electric and magnetic orthogonal static fields, we compute the conserved current density component and the quantized off-diagonal conductivity.

scholarly journals NEW TREATMENT OF THE NONCOMMUTATIVE DIRAC EQUATION WITH A COULOMB POTENTIAL

2012 ◽  
Vol 27 (19) ◽  
pp. 1250100 ◽  
Author(s):  
LAMINE KHODJA ◽  
SLIMANE ZAIM
Keyword(s):  
Magnetic Field ◽  
Field Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Hyperfine Structure ◽  
Coulomb Potential ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
New Treatment

Using the approach of the modified Euler–Lagrange field equation together with the corresponding Seiberg–Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification to the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the Hamiltonian of the hydrogen atom is obtained, and we show that the noncommutativity plays the role of spin and magnetic field which gives the hyperfine structure.

scholarly journals THE EXACT ELECTRON PROPAGATOR IN A MAGNETIC FIELD AS THE SUM OVER LANDAU LEVELS ON A BASIS OF THE DIRAC EQUATION EXACT SOLUTIONS

2011 ◽  
Vol 26 (16) ◽  
pp. 2725-2733 ◽  
Author(s):  
A. V. KUZNETSOV ◽  
A. A. OKRUGIN
Keyword(s):  
Magnetic Field ◽  
Dirac Equation ◽  
Exact Solutions ◽  
Landau Levels ◽  
Large Field ◽  
Quantum Processes ◽  
Direct Derivation ◽  
Calculation Technique ◽  
Further Development ◽  
The Magnetic Field

The exact propagator for an electron in a constant uniform magnetic field as the sum over Landau levels is obtained using the direct derivation by standard methods of quantum field theory from exact solutions to the Dirac equation in the magnetic field. The result can be useful for further development of the calculation technique of quantum processes in an external active medium, particularly in the conditions of moderately large field strengths when it is insufficient to take into account only the ground Landau level contribution.

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