scholarly journals Exact solutions of the (2+1) dimensional Dirac equation in a constant magnetic field in the presence of a minimal length

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
L. Menculini ◽  
O. Panella ◽  
P. Roy
Keyword(s):  
Magnetic Field ◽  
Dirac Equation ◽  
Exact Solutions ◽  
Constant Magnetic Field ◽  
Minimal Length

scholarly journals On the (2 + 1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty

2015 ◽  
Vol 24 (02) ◽  
pp. 1550016 ◽  
Author(s):  
P. Pedram ◽  
M. Amirfakhrian ◽  
H. Shababi
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Dirac Equation ◽  
General Solution ◽  
Harmonic Oscillator ◽  
Constant Magnetic Field ◽  
Minimal Length ◽  
Two Dimensional ◽  
Quantum Numbers ◽  
Dirac Hamiltonian

In this paper, we exactly solve the (2 + 1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two two-dimensional nonrelativistic harmonic oscillator and obtain the solutions without directly solving the corresponding differential equations which are presented by Menculini et al. [Phys. Rev. D 87 (2013) 065017]. We also show that Menculini et al. solution is a subset of the general solution which is related to the even quantum numbers.

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.

SOLUTION OF κ DEFORMED DIRAC EQUATION WITH ANOMALOUS MAGNETIC MOMENT INTERACTION

1995 ◽  
Vol 10 (26) ◽  
pp. 1969-1975 ◽  
Author(s):  
P. ROY ◽  
R. ROYCHOUDHURY
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Dirac Equation ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Constant Magnetic Field ◽  
Moment Interaction

We construct the deformed Dirac equation with anomalous magnetic moment interaction and solve this equation for a charged particle in the presence of a constant magnetic field.

scholarly journals Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
W. I. Skrypnik
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Coulomb Potential ◽  
Constant Magnetic Field ◽  
Equation Of Motion ◽  
Regular Polygons ◽  
Bounded Solutions ◽  
Infinite Time ◽  
Coulomb Type ◽  
Different Dimensions

The equation of motion in ℝ d of n generalized point charges interacting via the s -dimensional Coulomb potential, which contains for d = 2 a constant magnetic field, is considered. Planar exact solutions of the equation are found if either negative n − 1 > 2 charges and their masses are equal or n = 3 and the charges are different. They describe a motion of negative charges along identical orbits around the positive immobile charge at the origin in such a way that their coordinates coincide with vertices of regular polygons centered at the origin. Bounded solutions converging to an equilibrium in the infinite time for the considered equation without a magnetic field are also obtained. A condition permitting the existence of such solutions is proposed.

scholarly journals The exact solutions of a (2 + 1)-dimensional Dirac oscillator under a magnetic field in the presence of a minimal length

2015 ◽  
Vol 93 (5) ◽  
pp. 542-548 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Momentum Space ◽  
Uniform Magnetic Field ◽  
Hypergeometric Functions ◽  
Minimal Length ◽  
Wave Functions ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Energy Eigenvalues

Minimal length of a two-dimensional Dirac oscillator is investigated in the presence of a uniform magnetic field and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of hypergeometric functions.

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