scholarly journals Exact Solution of Dirac Equation with Charged Harmonic Oscillator in Electric Field: Bound States

2012 ◽  
Vol 03 (02) ◽  
pp. 170-179 ◽  
Author(s):  
Sameer M. Ikhdair
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Electric Field ◽  
Harmonic Oscillator ◽  
Bound States

scholarly journals Pseudospin Symmetry in the Relativistic Killingbeck Potential: Quasi-Exact Solution

2012 ◽  
Vol 67 (10-11) ◽  
pp. 567-571 ◽  
Author(s):  
Majid Hamzavi ◽  
Sameer M. Ikhdair ◽  
Karl-Erik Thylwe
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Harmonic Oscillator ◽  
Coulomb Potential ◽  
Particle Physics ◽  
Pseudospin Symmetry ◽  
Spin Symmetry ◽  
Cornell Potential ◽  
Special Cases

The Killingbeck potential consisting of the harmonic oscillator plus Cornell potential, ar2+br −c/r, is of great interest in particle physics. The solution of the Dirac equation with the Killingbeck potential is studied in the presence of the pseudospin (p-spin) symmetry within the context of quasiexact solutions. Two special cases of the harmonic oscillator and Coulomb potential are also discussed.

DYON–DYON BOUND STATES IN NON-RELATIVISTIC AND RELATIVISTIC FRAMEWORKS

1998 ◽  
Vol 13 (30) ◽  
pp. 5245-5256 ◽  
Author(s):  
B. S. RAJPUT ◽  
V. P. PANDEY
Keyword(s):  
Exact Solution ◽  
Angular Momentum ◽  
Dirac Equation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
The Other ◽  
System A ◽  
Relativistic Framework

Investigating dyon–dyon bound states in non-relativistic as well as in relativistic frameworks, it has been shown that in this system a dyon moves on a cone with its apex at the other dyon and axis along its angular momentum. Dyon–dyon bound states have been investigated in a non-relativistic framework to obtain energy eigenvalue and energy eigenfunction. It has also been shown that the exact solution of Dirac equation for this system is not possible due to the presence of a term vanishing more rapidly than r-1 in the potential of the system.

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 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).

scholarly journals Fermions in the Rindler spacetime

2019 ◽  
Vol 16 (09) ◽  
pp. 1950140 ◽  
Author(s):  
L. C. N. Santos ◽  
C. C. Barros
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Reference Frame ◽  
Bound States ◽  
Liouville Problem ◽  
External Potential ◽  
Compact Expression ◽  
Sturm Liouville

In this paper, we study the Dirac equation in the Rindler spacetime. The solution of the wave equation in an accelerated reference frame is obtained. The differential equation associated to this wave equation is mapped into a Sturm–Liouville problem of a Schrödinger-like equation. We derive a compact expression for the energy spectrum associated with the Dirac equation in an accelerated reference. It is shown that the noninertial effect of the accelerated reference frame mimics an external potential in the Dirac equation and, moreover, allows the formation of bound states.

scholarly journals INFLUENCE OF GRAVITY ON NONCOMMUTATIVE DIRAC EQUATION

2005 ◽  
Vol 20 (26) ◽  
pp. 1997-2005 ◽  
Author(s):  
SOFIANE BOUROUAINE ◽  
ACHOUR BENSLAMA
Keyword(s):  
Dirac Equation ◽  
Electric Field ◽  
Covariant Derivative ◽  
Strong Electric Field ◽  
Curved Spacetime ◽  
Tetrad Formalism ◽  
Dirac Particles ◽  
Modified Dirac Equation ◽  
New Form

In this paper, we investigate the influence of gravity and noncommutativity on Dirac particles. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved spacetime with an operator which depends on the noncommutative θ-parameter. As an application, we have computed the density number of the created particles in the presence of constant strong electric field in an anisotropic Bianchi universe.

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