scholarly journals Factorization of Dirac equation in two space dimensions

2014 ◽  
Vol 11 (04) ◽  
pp. 1450036 ◽  
Author(s):  
Hocine Bahlouli ◽  
Ahmed Jellal ◽  
Youness Zahidi
Keyword(s):  
Dirac Equation ◽  
Separation Of Variables ◽  
Scalar Potential ◽  
Complete Separation ◽  
Polar Coordinates ◽  
Dirac Spinor ◽  
Solvable Potentials ◽  
Scalar Type ◽  
Two Space Dimensions ◽  
Pseudo Scalar

We present a systematic approach for the separation of variables for the two-dimensional (2D) Dirac equation in polar coordinates. The three vector potential, which couple to the Dirac spinor via minimal coupling, along with the scalar potential are chosen to have angular dependence which emanate the Dirac equation to complete separation of variables. Exact solutions are obtained for a class of solvable potentials along with their relativistic spinor wavefunctions. Particular attention is paid to the situation where the potentials are confined to a quantum dot region and are of scalar, vector and pseudo-scalar type. The study of a single charged impurity embedded in a 2D Dirac equation in the presence of a uniform magnetic field was treated as a particular case of our general study.

Solution of the Dirac equation with magnetic monopole and pseudoscalar potentials

Open Physics ◽  
2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Sohrab Aghaei ◽  
Alireza Chenaghlou
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Spherical Harmonics ◽  
Coulomb Potential ◽  
Magnetic Monopole ◽  
Separation Of Variables ◽  
Scalar Potential ◽  
Bohm Potential ◽  
Pseudo Scalar ◽  
Aharonov Bohm

AbstractThe Dirac equation in the presence of the Dirac magnetic monopole potential, the Aharonov-Bohm potential, a Coulomb potential and a pseudo-scalar potential, is solved by separation of variables using the spinweighted spherical harmonics. The energy spectrum and the form of the spinor functions are obtained. It is shown that the number j in spin-weighted spherical harmonics must be greater than $$\left| q \right| - \tfrac{1} {2}$$.

scholarly journals Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field

2018 ◽  
Vol 15 (05) ◽  
pp. 1850085 ◽  
Author(s):  
A. V. Shapovalov ◽  
A. I. Breev
Keyword(s):  
Dirac Equation ◽  
Separation Of Variables ◽  
Flat Space ◽  
External Electromagnetic Field ◽  
Complete Separation ◽  
Electromagnetic Potential ◽  
First Order ◽  
Matrix Coefficients ◽  
Symmetry Operators ◽  
Differential Symmetry

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a [Formula: see text]-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a [Formula: see text]-dimensional Minkowski (flat) space. For each of the sets, we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.

scholarly journals DIRAC SPINOR IN A NONSTATIONARY GÖDEL-TYPE COSMOLOGICAL UNIVERSE

1993 ◽  
Vol 08 (32) ◽  
pp. 3011-3015 ◽  
Author(s):  
VÍCTOR M. VILLALBA
Keyword(s):  
Dirac Equation ◽  
Frequency Spectrum ◽  
Rotational Speed ◽  
Separation Of Variables ◽  
Dirac Spinor ◽  
Dirac Particles

In this letter we solve, via separation of variables, the massless Dirac equation in a nonstationary rotating, causal Gödel-type cosmological universe, having a constant rotational speed in all the points of the space. We compute the frequency spectrum. We show that the spectrum of massless Dirac particles is discrete and unbounded.

Dirac particle in electric field with confining scalar potential on (anti)-de Sitter background

2018 ◽  
Vol 33 (34) ◽  
pp. 1850202 ◽  
Author(s):  
N. Messai ◽  
B. Hamil ◽  
A. Hafdallah
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Electric Field ◽  
Scalar Potential ◽  
Dirac Particle ◽  
Wave Functions ◽  
De Sitter ◽  
Sitter Background ◽  
Position Representation

In this paper, we study the (1 + 1)-dimensional Dirac equation in the presence of electric field and scalar linear potentials on (anti)-de Sitter background. Using the position representation, the energy spectrum and the corresponding wave functions are exactly obtained.

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