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.

THE MASSLESS BOUND STATE FORMALISM IN TWO-PARTICLE RELATIVISTIC QUANTUM MECHANICS

1988 ◽  
Vol 03 (05) ◽  
pp. 1235-1261 ◽  
Author(s):  
H. SAZDJIAN
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Bound State ◽  
Relativistic Quantum Mechanics ◽  
Composite Systems ◽  
Bound State Case ◽  
State Case

We develop, in the framework of two-particle relativistic quantum mechanics, the formalism needed to describe massless bound state systems and their internal dynamics. It turns out that the dynamics here is two-dimensional, besides the contribution of the spin degrees of freedom, provided by the two space-like transverse components of the relative coordinate four-vector, decomposed in an appropriate light cone basis. This is in contrast with the massive bound state case, where the dynamics is three-dimensional. We also construct the scalar product of the theory. We apply this formalism to several types of composite systems, involving spin-0 bosons and/or spin-1/2 fermions, which produce massless bound states.

scholarly journals Generalized KG-oscillator with a uniform magnetic field under the influence of Coulomb-type potentials in cosmic string space-time and Aharonov-Bohm effect

2021 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Magnetic Field ◽  
Cosmic String ◽  
Uniform Magnetic Field ◽  
Bound States ◽  
Space Time ◽  
Vector Potentials ◽  
Klein Gordon ◽  
Relativistic Analogue ◽  
Bohm Effect ◽  
Aharonov Bohm

We solve a generalized Klein-Gordon oscillator (KGO) in the presence of a uniform magnetic field including quantum flux under the effects of a scalar and vector potentials of Coulomb-types in the static cosmic string space-time. We obtain the energy and corresponding eigenfunctions, and analyze a relativistic analogue of the Aharonov-Bohm effect for bound states.

OCTONIC FIRST-ORDER EQUATIONS OF RELATIVISTIC QUANTUM MECHANICS

2009 ◽  
Vol 24 (22) ◽  
pp. 4157-4167 ◽  
Author(s):  
VICTOR L. MIRONOV ◽  
SERGEY V. MIRONOV
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Maxwell Equations ◽  
Relativistic Quantum ◽  
Order Equation ◽  
Second Order ◽  
Relativistic Quantum Mechanics ◽  
Quantum Fields ◽  
First Order ◽  
Spatial Operators

We demonstrate a generalization of relativistic quantum mechanics using eight-component octonic wave function and octonic spatial operators. It is shown that the second-order equation for octonic wave function describing particles with spin 1/2 can be reformulated in the form of a system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special types of wave functions the second-order equation can be reduced to the single first-order equation analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not have quantum fields.

Aharonov–Bohm effect for bound states on spin-0 scalar charged particles in a rotating cosmic string space–time with Coulomb potentials

2020 ◽  
Vol 35 (20) ◽  
pp. 2050101
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Cosmic String ◽  
Quantum Dynamics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Charged Particles ◽  
Topological Defects ◽  
Space Time ◽  
Vector Potentials ◽  
Bohm Effect ◽  
Aharonov Bohm

In this paper, we study the relativistic quantum dynamics of spin-0 scalar charged particles with a magnetic quantum flux produced by topological defects in a rotating cosmic string space–time. We solve the Klein–Gordon equation subject to Coulomb-type scalar and vector potentials in the considered framework and obtain the energy eigenvalues and eigenfunctions and analyze the analogue effect to Aharonov–Bohm effect for bound states.

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.

Electron propagator solution for an inhomogeneous magnetic field in the momentum space representation

2020 ◽  
Vol 35 (25) ◽  
pp. 2050150
Author(s):  
H. Hamdi ◽  
H. Benzair
Keyword(s):  
Magnetic Field ◽  
Momentum Space ◽  
Relativistic Quantum ◽  
Inhomogeneous Magnetic Field ◽  
Relativistic Quantum Mechanics ◽  
Space Representation ◽  
Integral Formalism ◽  
Field Problem ◽  
Energy Eigenvalues ◽  
Transformation Methods

The relativistic quantum mechanics of the electron in an inhomogeneous magnetic field problem is solved exactly in terms of the momentum space path integral formalism. We adopt the space–time transformation methods, which are [Formula: see text]-point discretization dependent, to evaluate quantum corrections. The propagator is calculated, the energy eigenvalues and their associated curves are illustrated. The limit case is then deduced for a small parameter.

scholarly journals LORENTZ BOOSTED NN POTENTIAL FOR FEW-BODY SYSTEMS: APPLICATION TO THE THREE-NUCLEON BOUND STATE

2003 ◽  
Vol 18 (02n06) ◽  
pp. 124-127 ◽  
Author(s):  
H. KAMADA ◽  
W. GLÖCKLE ◽  
J. GOLAK ◽  
CH. ELSTER
Keyword(s):  
Quantum Mechanics ◽  
Binding Energy ◽  
Schrodinger Equation ◽  
Relativistic Quantum ◽  
Bound State ◽  
Nucleon Nucleon ◽  
Relativistic Quantum Mechanics ◽  
Equal Time ◽  
Momentum Change ◽  
Approximate Scheme

In the context of equal time relativistic quantum mechanics we introduce a Lorentz boosted potential. The dynamical input are nonrelativistic realistic nucleon-nucleon (NN) potentials, which by a suitable momentum change are analytically transformed into NN potentials fulfilling the relativistic two-nucleon Schrödinger equation in the c.m. system. The binding energy of the three nucleon (3N) bound state is calculated and we find that the boost effects for the two-body subsystems are repulsive and lower the binding energy. In addition we compare to a recently proposed approximate scheme.

Nuclear Physics Methods for Problems in Relativistic Quantum Mechanics

1998 ◽  
Vol 07 (05) ◽  
pp. 559-571
Author(s):  
Marcos Moshinsky ◽  
Verónica Riquer
Keyword(s):  
Quantum Mechanics ◽  
Nuclear Physics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Negative Energy ◽  
Relativistic Quantum Mechanics ◽  
Variational Parameter ◽  
Approximate Methods ◽  
Rest Energy ◽  
Quark Models

Atomic and molecular physicists have developed extensive and detailed approximate methods for dealing with the relativistic versions of the Hamiltonians appearing in their fields. Nuclear physicists were originally more concerned with non-relativistic problems as the energies they were dealing with were normally small compared with the rest energy of the nucleon. This situation has changed with the appearance of the quark models of nucleons and thus the objective of this paper is to use the standard variational procedures of nuclear physics for problems in relativistic quantum mechanics. The 4 × 4α and β matrices in the Dirac equation are replaced by 2 × 2 matrices, one associated with ordinary spin and the other, which we call sign spin, is mathematically identical to the isospin of nuclear physics. The states on which our Hamiltonians will act will be the usual harmonic oscillator ones with ordinary and sign spin and the frequency ω of the oscillator will be our only variational parameter. The example discussed as an illustration will still be the Coulomb problem as the exact energies of the relativistic bound states are available for comparison. A gap of the order of 2mc2 is observed between states of positive and negative energy, that permits the former to be compared with the exact results.

scholarly journals Spin-0 scalar particle interacts with scalar potential in the presence of magnetic field and quantum flux under the effects of KKT in 5D cosmic string spacetime

2020 ◽  
pp. 2150004
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Magnetic Field ◽  
Quantum Dynamics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Particle ◽  
Klein Theory ◽  
Klein Gordon ◽  
Quantum Flux

In this paper, we study a relativistic quantum dynamics of spin-0 scalar particle interacts with scalar potential in the presence of a uniform magnetic field and quantum flux in background of Kaluza–Klein theory (KKT). We solve Klein–Gordon equation in the considered framework and analyze the relativistic analogue of the Aharonov–Bohm effect for bound states. We show that the energy levels depend on the global parameters characterizing the spacetime, scalar potential and the magnetic field which break their degeneracy.

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