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 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.

ON A RESULT CONCERNING THE BEHAVIOR OF A RELATIVISTIC QUANTUM SYSTEM IN THE COSMIC STRING SPACETIME

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1549-1556 ◽  
Author(s):  
V. B. BEZERRA ◽  
GEUSA DE A. MARQUES
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Quantum System ◽  
Relativistic Electron ◽  
Coulomb Potential ◽  
Cosmic String ◽  
Relativistic Quantum

We consider the problem of a relativistic electron in the presence of a Coulomb potential and a magnetic field in the background spacetime corresponding to a cosmic string. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle.

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.

Particule de spin-1 dans un potentiel d’Aharonov–Bohm

2007 ◽  
Vol 85 (12) ◽  
pp. 1417-1429 ◽  
Author(s):  
A Boumali
Keyword(s):  
Energy Spectrum ◽  
Wave Functions ◽  
Three Dimensions ◽  
Bohm Potential ◽  
Relativistic Spin ◽  
Bohm Effect ◽  
Aharonov Bohm

In this article we solved the problem of the relativistic spin-1 particle in the presence of the Aharonov–Bohm potential in two and three dimensions, while using the Duffin–Kemmer–Petiau equation. The wave functions as well as the energy spectrum, in both cases, have been obtained. The validity of the Pauli criterion in the Aharonov–Bohm effect is well discussed.

EXACT SOLUTIONS OF THE DIRAC EQUATION WITH A COULOMB PLUS SCALAR POTENTIAL IN 2 + 1 DIMENSIONS

2002 ◽  
Vol 11 (06) ◽  
pp. 483-489 ◽  
Author(s):  
SHI-HAI DONG ◽  
XIAO-YAN GU ◽  
ZHONG-QI MA ◽  
SHISHAN DONG
Keyword(s):  
Dirac Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Coulomb Potential ◽  
Scalar Potential ◽  
Second Order ◽  
First Order ◽  
Second Order Differential Equations

The exact solutions of the (2+1)-dimensional Dirac equation with a Coulomb potential and a scalar one are analytically presented by studying the second-order differential equations obtained from a pair of coupled first-order ones. The eigenvalues are studied in some detail.

scholarly journals Dirac Equation in the Presence of Hartmann and Ring-Shaped Oscillator Potentials

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Zahra Bakhshi
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Bound States ◽  
Scalar Potential ◽  
Solvable Models ◽  
Nonrelativistic Quantum ◽  
Physical Conditions ◽  
Basic Model ◽  
Nonrelativistic Quantum Mechanics

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrödinger-like equation obtained by Dirac equation with the nonrelativistic solvable models is the most efficient method. By this technique, the exact relativistic solutions of Dirac equation for Hartmann and Ring-Shaped Oscillator Potentials are accessible, when the scalar potential is equal to the vector potential. Using solvable nonrelativistic quantum mechanics systems as a basic model and considering the physical conditions provide the changes in the restrictions of relativistic parameters based on the nonrelativistic definitions of parameters.

scholarly journals Exact solutions of the 2D Dunkl–Klein–Gordon equation: The Coulomb potential and the Klein–Gordon oscillator

2021 ◽  
pp. 2150171
Author(s):  
R. D. Mota ◽  
D. Ojeda-Guillén ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Angular Momentum ◽  
Energy Spectrum ◽  
Exact Solutions ◽  
Coulomb Potential ◽  
Gordon Equation ◽  
Separation Of Variables ◽  
Point Of View ◽  
Algebraic Point ◽  
Klein Gordon ◽  
Klein Gordon Equation

We introduce the Dunkl–Klein–Gordon (DKG) equation in 2D by changing the standard partial derivatives by the Dunkl derivatives in the standard Klein–Gordon (KG) equation. We show that the generalization with Dunkl derivative of the z-component of the angular momentum is what allows the separation of variables of the DKG equation. Then, we compute the energy spectrum and eigenfunctions of the DKG equations for the 2D Coulomb potential and the Klein–Gordon oscillator analytically and from an su(1, 1) algebraic point of view. Finally, we show that if the parameters of the Dunkl derivative vanish, the obtained results suitably reduce to those reported in the literature for these 2D problems.

scholarly journals EXACT SPIN AND PSEUDO-SPIN SYMMETRIC SOLUTIONS OF THE DIRAC–KRATZER PROBLEM WITH A TENSOR POTENTIAL VIA LAPLACE TRANSFORM APPROACH

2012 ◽  
Vol 27 (30) ◽  
pp. 1250171 ◽  
Author(s):  
ALTUĞ ARDA ◽  
RAMAZAN SEVER
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Laplace Transform ◽  
Coulomb Potential ◽  
Spin Symmetry ◽  
Bound State ◽  
Exact Bound ◽  
Tensor Potential ◽  
The Laplace Transform ◽  
Parameter Values

Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectrum is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agreement with the ones given in the literature. The numerical results are also given in a table for different parameter values.

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