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.

scholarly journals Self-Adjoint Extension Approach to Motion of Spin-1/2 Particle in the Presence of External Magnetic Fields in the Spinning Cosmic String Spacetime

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 203
Author(s):  
Márcio M. Cunha ◽  
Edilberto O. Silva
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Magnetic Fields ◽  
Cosmic String ◽  
Relativistic Quantum ◽  
Wave Functions ◽  
The Self ◽  
Extension Method ◽  
Adjoint Extension ◽  
Quantum Motion

In this work, we study the relativistic quantum motion of an electron in the presence of external magnetic fields in the spinning cosmic string spacetime. The approach takes into account the terms that explicitly depend on the particle spin in the Dirac equation. The inclusion of the spin element in the solution of the problem reveals that the energy spectrum is modified. We determine the energies and wave functions using the self-adjoint extension method. The technique used is based on boundary conditions allowed by the system. We investigate the profiles of the energies found. We also investigate some particular cases for the energies and compare them with the results in the literature.

POLYNOMIAL SOLUTIONS OF HEUN EQUATION DESCRIBING FERMIONS IN GRAPHENE

2013 ◽  
Vol 27 (32) ◽  
pp. 1350190 ◽  
Author(s):  
MARINA-AURA DARIESCU ◽  
CIPRIAN DARIESCU
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Current Density ◽  
Hermite Polynomials ◽  
Heun Equation ◽  
Conserved Current ◽  
Familiar Form ◽  
The Magnetic Field ◽  
Massless Fermions

The wavefunctions describing the massless fermions evolving in a static magnetic field orthogonal to a radially planar electric field are obtained, as solutions to Dirac equation. In the case of the magnetic field alone, the corresponding HeunB confluent functions turn into the usual Hermite polynomials and the energy spectrum has the familiar form which has been reported for graphene samples. Within a more involved analysis with both electric and magnetic orthogonal static fields, we compute the conserved current density component and the quantized off-diagonal conductivity.

scholarly journals NEW TREATMENT OF THE NONCOMMUTATIVE DIRAC EQUATION WITH A COULOMB POTENTIAL

2012 ◽  
Vol 27 (19) ◽  
pp. 1250100 ◽  
Author(s):  
LAMINE KHODJA ◽  
SLIMANE ZAIM
Keyword(s):  
Magnetic Field ◽  
Field Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Hyperfine Structure ◽  
Coulomb Potential ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
New Treatment

Using the approach of the modified Euler–Lagrange field equation together with the corresponding Seiberg–Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification to the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the Hamiltonian of the hydrogen atom is obtained, and we show that the noncommutativity plays the role of spin and magnetic field which gives the hyperfine structure.

Scattering states of Dirac equation in the presence of cosmic string for Coulomb interaction

2015 ◽  
Vol 30 (21) ◽  
pp. 1550124 ◽  
Author(s):  
M. Hosseinpour ◽  
H. Hassanabadi
Keyword(s):  
Electromagnetic Field ◽  
Dirac Equation ◽  
Coulomb Interaction ◽  
Coulomb Potential ◽  
Cosmic String ◽  
Phase Shifts ◽  
Space Time ◽  
Radial Part ◽  
Scattering States ◽  
Scalar Potentials

We study the covariant Dirac equation in the space–time generated by a cosmic string in presence of vector and scalar potentials of electromagnetic field. We obtain the solution of the radial part of Dirac equation. We consider the scattering states under the Coulomb potential and obtain the phase shifts.

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 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.

scholarly journals Relativistic Quantum Motion of an Electron in Spinning Cosmic String Spacetime in the Presence of Uniform Magnetic Field and Aharonov-Bohm Potential

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Márcio M. Cunha ◽  
Edilberto O. Silva
Keyword(s):  
Magnetic Field ◽  
Cosmic String ◽  
Bound States ◽  
Relativistic Quantum ◽  
Bound State ◽  
Order Equation ◽  
Second Order ◽  
Relativistic Quantum Mechanics ◽  
Physical Parameters ◽  
Aharonov Bohm

In this manuscript, we study the relativistic quantum mechanics of an electron in external fields in the spinning cosmic string spacetime. We obtain the Dirac equation and write the first- and second-order equations from it, and then, we solve these equations for bound states. We show that there are bound state solutions for the first-order equation Dirac. For the second-order equation, we obtain the corresponding wave functions, which depend on the Kummer functions. Then, we determine the energies of the particle. We examine the behavior of the energies as a function of the physical parameters of the model, such as rotation, curvature, magnetic field, Aharonov-Bohm flux, and quantum numbers. We find that, depending on the values of these parameters, there are energy nonpermissible levels.

Introduction to Relativistic Quantum Chemistry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Dirac Equation ◽  
Quantum Chemistry ◽  
Relativistic Theory ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Basis Sets ◽  
Spin Orbit ◽  
Approximate Methods ◽  
Nonrelativistic Theory

This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

scholarly journals The measurement of the energy of cosmic rays - II—The curvature measurements and the energy spectrum

1936 ◽  
Vol 154 (883) ◽  
pp. 573-587 ◽  
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Cosmic Rays ◽  
Magnetic Fields ◽  
Strong Magnetic Fields ◽  
The Earth ◽  
Primary Particles ◽  
Curvature Measurements

Both the penetrating power of the cosmic rays through material ab­sorbers and their ability to reach the earth in spite of its magnetic field, make it certain that the energy of many of the primary particles must reach at least 10 11 e-volts. However, the energy measurements by Kunze, and by Anderson, using cloud chambers in strong magnetic fields, have extended only to about 5 x 10 9 e-volts. Particles of greater energy were reported, but the curvature of their tracks was too small to be measured with certainty. We have extended these energy measurements to somewhat higher energies, using a large electro-magnet specially built for the purpose and described in Part I. As used in these experiments, the magnet allowed the photography of tracks 17 cm long in a field of about 14,000 gauss. The magnet weighed about 11,000 kilos and used a power of 25 kilowatts.

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