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 Relativistic Two-Dimensional Harmonic Oscillator Plus Cornell Potentials in External Magnetic and AB Fields

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sameer M. Ikhdair ◽  
Ramazan Sever
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Ansatz Method ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
Klein Gordon ◽  
Aharonov Bohm ◽  
Potential Parameters

The Klein-Gordon (KG) equation for the two-dimensional scalar-vector harmonic oscillator plus Cornell potentials in the presence of external magnetic and Aharonov-Bohm (AB) flux fields is solved using the wave function ansatz method. The exact energy eigenvalues and the wave functions are obtained in terms of potential parameters, magnetic field strength, AB flux field, and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL= 0) and AB flux field (ξ=0) cases. Effect of external fields on the nonrelativistic energy eigenvalues and wave function solutions is also precisely presented. Some special cases like harmonic oscillator and Coulombic fields are also studied.

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.

scholarly journals Thermal properties of a two-dimensional Duffin–Kemmer–Petiau oscillator under an external magnetic field in the presence of a minimal length

2020 ◽  
Vol 35 (33) ◽  
pp. 2050278
Author(s):  
H. Aounallah ◽  
B. C. Lütfüoğlu ◽  
J. Kříž
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Energy Eigenvalue ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Summation Formula ◽  
Minimal Length ◽  
Two Dimensional ◽  
Relativistic Limit ◽  
Ordinary Quantum

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

Highly accurate analytical energy of a two-dimensional exciton in a constant magnetic field

2016 ◽  
Vol 495 ◽  
pp. 16-20 ◽  
Author(s):  
Ngoc-Tram D. Hoang ◽  
Duy-Anh P. Nguyen ◽  
Van-Hung Hoang ◽  
Van-Hoang Le
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Two Dimensional
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