Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations

2016 ◽  
Author(s):  
I. A. Assi ◽  
H. Bahlouli ◽  
A. D. Alhaidari
Keyword(s):  
Dirac Equation ◽  
Tridiagonal Matrix ◽  
Matrix Representations ◽  
Solvable Potentials

Solvable potentials in pseudo-hermetic Dirac equation with PT symmetry

2021 ◽  
Author(s):  
Fereshte Soliemani ◽  
Zahra Bakhshi
Keyword(s):  
Dirac Equation ◽  
Pt Symmetry ◽  
Solvable Potentials

scholarly journals Symmetries of Relativistic Hydrogen Atom

2019 ◽  
Vol 64 (12) ◽  
pp. 1148
Author(s):  
V. M. Simulik ◽  
I. O. Gordievich
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation ◽  
Spinor Field ◽  
Coulomb Field ◽  
Matrix Representations ◽  
Pure Matrix ◽  
Symmetry Operators ◽  
Non Local ◽  
Relativistic Hydrogen ◽  
Relativistic Hydrogen Atom

The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are found. Two different bosonic realizations of this algebra are found as well. All generators of the above-mentioned algebras commute with the operator of the Dirac equation in an external Coulomb field and, therefore, determine the algebras of invariance of such Dirac equation. Hence, the spin s = (1, 0) Bose symmetry of the Dirac equation for the free spinor field, proved recently in our papers, is extended here for the Dirac equation interacting with an external Coulomb field. A relativistic hydrogen atom is modeled by such Dirac equation. We are able to prove for the relativistic hydrogen atom both the fermionic and bosonic symmetries known from our papers in the case of a non-interacting spinor field. New symmetry operators are found on the basis of new gamma matrix representations of the Clifford and SO(8) algebras, which are known from our recent papers as well. Hidden symmetries were found both in the canonical Foldy–Wouthuysen and covariant Dirac representations. The found symmetry operators, which are pure matrix ones in the Foldy–Wouthuysen representation, become non-local in the Dirac model.

Dirac Equation and Ground State of Solvable Potentials: Supersymmetry Method

2011 ◽  
Vol 50 (9) ◽  
pp. 2811-2818 ◽  
Author(s):  
H. Panahi ◽  
Z. Bakhshi
Keyword(s):  
Dirac Equation ◽  
Ground State ◽  
Solvable Potentials

scholarly journals Solving Dirac equation using the tridiagonal matrix representation approach

2016 ◽  
Vol 380 (18-19) ◽  
pp. 1577-1581 ◽  
Author(s):  
A.D. Alhaidari ◽  
H. Bahlouli ◽  
I.A. Assi
Keyword(s):  
Dirac Equation ◽  
Matrix Representation ◽  
Tridiagonal Matrix ◽  
Tridiagonal Matrix Representation

scholarly journals Tridiagonal matrix representations of cyclic self-adjoint operators. II

1985 ◽  
Vol 120 (1) ◽  
pp. 47-53 ◽  
Author(s):  
Joanne Dombrowski
Keyword(s):  
Tridiagonal Matrix ◽  
Matrix Representations ◽  
Adjoint Operators

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 and the Solvable Potentials in the Schrodinger Equation

2011 ◽  
Author(s):  
Z. Bakhshi ◽  
H. Panahi ◽  
Muhammed Hasan Aslan ◽  
Ahmet Yayuz Oral ◽  
Mehmet Özer ◽  
...  
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Solvable Potentials

Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner's Classification

2013 ◽  
Vol 60 (3) ◽  
pp. 296-302 ◽  
Author(s):  
S. Aghaei ◽  
A. Chenaghlou
Keyword(s):  
Dirac Equation ◽  
Solvable Potentials
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