scholarly journals Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential

2017 ◽  
Vol 58 (11) ◽  
pp. 113507 ◽  
Author(s):  
Axel Schulze-Halberg ◽  
Pinaki Roy
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Two Dimensional ◽  
Scarf Potential ◽  
Energy Dependent

ALGEBRAIC APPROACH TO SPIN SYMMETRY FOR THE DIRAC EQUATION WITH THE TRIGONOMETRIC SCARF POTENTIAL

2010 ◽  
Vol 25 (08) ◽  
pp. 1649-1659 ◽  
Author(s):  
GAO-FENG WEI ◽  
XIAO-YONG DUAN ◽  
XU-YANG LIU
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Algebraic Approach ◽  
Spin Symmetry ◽  
Positive Energy ◽  
Scarf Potential ◽  
Vector Case ◽  
Energy Bound ◽  
Spinor Wave

By a simple algebraic approach we study the exact solution to the Dirac equation with scalar and vector trigonometric Scarf potentials in the case of spin symmetry. The transcendental energy equation and spinor wave functions are presented. It is found that there exist only positive energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter α goes to zero. The equally scalar and vector case is studied briefly.

Bound States in Two-dimensional Crossed or Bent Quantum Wires

1998 ◽  
Vol 12 (19) ◽  
pp. 1907-1919 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Conformal Transformation ◽  
Bound States ◽  
Dirichlet Boundary ◽  
Quantum Wires ◽  
Bound State ◽  
Two Dimensional ◽  
State Problem ◽  
Bound State Problem ◽  
Energy Dependent ◽  
Sharp Corners

The method of conformal transformation is applied to solve the bound state problem for two-dimensional crossed wires with sharp and with smooth circular corners, for T-shaped and L-shaped wires and a number of other geometries. It is shown that in this method the wave equation with Dirichlet boundary condition on the boundaries of these wires can be transformed to a Schrödinger equation with a unique two-dimensional energy-dependent noneseparable potential. The results for various geometries indicate that sharp corners are essential in generating the bound states.

BOUND STATES AND KLEIN PARADOX OF GRAPHENE SYSTEMS IN CONFINING POTENTIALS

2012 ◽  
Vol 26 (17) ◽  
pp. 1250108
Author(s):  
HAI HUANG ◽  
XIA HUANG
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Bound State ◽  
Linear Potential ◽  
Two Dimensional ◽  
Potential Well ◽  
Klein Paradox ◽  
Confining Potential ◽  
Potential Depth

Two-dimensional massive Dirac equation in both potential well and linear potential is discussed. We find that in the case of potential well, the bound states disappear from the spectrum for large enough potential depth. With the linear confining potential, we show that the Dirac equation presents no bound state. Both these results can be identified as fine examples of the Klein paradox. Applications to graphene systems are also discussed.

scholarly journals Fast forwad Adiabatic Quantum Dynamics On Two Dimensional Dirac Equation

2021 ◽  
Vol 1842 (1) ◽  
pp. 012057
Author(s):  
I Setiawan ◽  
R Sugihakim ◽  
B E Gunara
Keyword(s):  
Dirac Equation ◽  
Quantum Dynamics ◽  
Two Dimensional

scholarly journals TOPOLOGICAL INSULATOR AND THE DIRAC EQUATION

SPIN ◽  
2011 ◽  
Vol 01 (01) ◽  
pp. 33-44 ◽  
Author(s):  
SHUN-QING SHEN ◽  
WEN-YU SHAN ◽  
HAI-ZHOU LU
Keyword(s):  
Dirac Equation ◽  
Topological Insulator ◽  
Bound States ◽  
Topological Insulators ◽  
Mass Term ◽  
Point Of View ◽  
Quadratic Term ◽  
General Description ◽  
Dirac Equations ◽  
Topological Quantum

We present a general description of topological insulators from the point of view of Dirac equations. The Z2 index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, i.e., m → m − Bp2, the Z2 index is modified as 1 for mB > 0 and 0 for mB < 0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a nontrivial system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation is obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z2 index we establish a relation between the Dirac equation and topological insulators.

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 Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshghi ◽  
M. Hamzavi ◽  
S. M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Laplace Transformation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Coulomb Field ◽  
Transformation Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Dependent Mass ◽  
Laplace Transformation Method

The spatially dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction (T=0).

Bound states at impurities in a two-dimensional metal

2005 ◽  
Vol 72 (3) ◽  
pp. 430-436 ◽  
Author(s):  
E Dupont-Ferrier ◽  
P Mallet ◽  
L Magaud ◽  
J. Y Veuillen
Keyword(s):  
Bound States ◽  
Two Dimensional
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