scholarly journals Bound Electron Transitions under the Influence of Electromagnetic Wave in Constant Magnetic Field

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1367
Author(s):  
Vladimir Zhukovsky
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Quantum Wells ◽  
Wave Equations ◽  
Gordon Equation ◽  
Classical Equation ◽  
Relativistic Case ◽  
Radiative Transitions ◽  
Klein Gordon ◽  
Klein Gordon Equation

Motion and radiative transitions of an electron in a magnetic field under the influence of an external electromagnetic wave are studied for various confining conditions in semiconductor, graphene, in quantum wells, and relativistic generalization in terms of the Klein–Gordon equation are considered. In particular, the following problems are discussed. The so-called cyclotron resonance, which may appear in graphene, is studied with indication for appearance of the so-called frequency-halving. The problem is solved for two-dimensional massless charged particle, whose gapless nature is protected by sublattice symmetry. The exact classical calculation of this effect is undertaken in the framework of a 2D classical equation for a zero-mass electron. We also find an exact solution of the Schrödinger equation for charge carriers in semiconductors under the influence of an external magnetic field and in the field of electromagnetic wave with an account for their radiative transitions. Solutions of the relativistic Klein–Gordon equation in this configuration of electromagnetic fields are found as a certain generalization of the results obtained for the non-relativistic case. These results may serve as a first step for further efforts to find exact solutions of wave equations for quasiparticles in solid state structures in external fields.

Electromagnetic interaction with the Klein–Gordon equation in the framework of GUP

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
B. Khosropour
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Uncertainty Principle ◽  
Electric Potential ◽  
Uniform Magnetic Field ◽  
Gordon Equation ◽  
Electromagnetic Interaction ◽  
Generalized Uncertainty Principle ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this work, according to the generalized uncertainty principle, we study the Klein–Gordon equation interacting with the electromagnetic field. The generalized Klein–Gordon equation is obtained in the presence of a scalar electric potential and a uniform magnetic field. Furthermore, we find the relation of the generalized energy–momentum in the presence of a scalar electric potential and a uniform magnetic field separately.

scholarly journals Klein-Gordon Equation and Wave Function in Robertson-Walker and Schwarzschild space-tim

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Wave Equations ◽  
Gordon Equation ◽  
Space Time ◽  
Wave Functions ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Gauge Fixing ◽  
Klein Gordon ◽  
Klein Gordon Equation

In the general relativity theory, we find Klein-Gordon wave functions in Robertson-Walker and Schwarzschild space-time. Specially, this article is that Klein-Gordon wave equations is treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

scholarly journals EFFECTIVE MASS KLEIN-GORDON EQUATION WITH POSITION DEPENDENT MAGNETIC FIELD

2019 ◽  
Vol 2 (1) ◽  
pp. 32-35
Author(s):  
ÖZGÜR MIZRAK ◽  
OKTAY AYDOĞDU ◽  
KENAN SÖĞÜT
Keyword(s):  
Magnetic Field ◽  
Effective Mass ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Theoretical Investigation of Subluminal Particles Endowed with Imaginary Mass

2021 ◽  
Author(s):  
Luca Nanni
Keyword(s):  
General Solution ◽  
Wave Packet ◽  
Boundary Conditions ◽  
Theoretical Investigation ◽  
Wave Equations ◽  
Gordon Equation ◽  
Fourier Integral ◽  
Klein Gordon ◽  
Group Velocities ◽  
Klein Gordon Equation

In this article, the general solution of the tachyonic Klein-Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex \omega-plane. In particular, it is proved that under given boundary conditions this solution does not contain any superluminal components. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that for enough small energies it behaves as a localized wave.

Gravity

2017 ◽  
Vol 13 (2) ◽  
pp. 4689-4691
Author(s):  
Jim Goodman
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electric Potential ◽  
Gravitational Constant ◽  
Gordon Equation ◽  
Relativistic Correction ◽  
Equation Solution ◽  
Klein Gordon ◽  
The Magnetic Field ◽  
Klein Gordon Equation

Considering two balls of Z protons each near each other the residual electric potential V is calculated. Also the gravitational potential is calculated. The Gravitational constant is the same for both. Thus the electric field creates gravity. This calculation is possible because the multibody energy states are known exactly. The relativistic correction of 2 has been found from the Klein-Gordon Equation solution. This finding is an important step in reducing known forces to one field. Recall the electric field is generated by motion in the magnetic field of atoms of a magnetic dipole.  The mass is a function of the length of the magnetic dipole.

scholarly journals Theoretical Investigation of Subluminal Particles Endowed with Imaginary Mass

Particles ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 325-332
Author(s):  
Luca Nanni
Keyword(s):  
General Solution ◽  
Wave Packet ◽  
Boundary Conditions ◽  
Wave Equations ◽  
Gordon Equation ◽  
Fourier Integral ◽  
Klein Gordon ◽  
The Given ◽  
Group Velocities ◽  
Klein Gordon Equation

In this article, the general solution of the tachyonic Klein–Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex ω-plane. In particular, it is proved that this solution does not contain any superluminal components under the given boundary conditions. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of the neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that it behaves as a localized wave for sufficiently small energies.

The Klein-Gordon Equation

2017 ◽  
Vol 13 (2) ◽  
pp. 4648-4650
Author(s):  
Jim Goodman
Keyword(s):  
Magnetic Field ◽  
Hilbert Space ◽  
Group Theory ◽  
Gordon Equation ◽  
Relativistic Correction ◽  
Usual Solution ◽  
Klein Gordon ◽  
A Charge ◽  
Klein Gordon Equation

Two solutions to the Klein-Gordon equation are found. The existence of a maximum relativistic correction of 2 is thus indicated. The normal relativistic correction is given by the usual solution. A certain Hilbert Space is used to find the solutions using a group theory taught at LSU and the Texas Method of Math also taught at LSU. The usefulness of group theoretical manipulations in Hilbert Space is indicated. A lemma is proved using this group theory that predicts a charge of +/-1 is the only values of charge possible. The usefulness of the second solution to the Klein-Gordon equation of a maximum of 2 for the relativistic correction is basic to the mass predictions in [3]. The fact that the energy reaches mc^2 indicates a dipole spinning at velocity c. The dipole is spinning in a magnetic field created by other particles so it creates charge.

Spinless Particle in a Magnetic Field Under Minimal Length Scenario

2016 ◽  
Vol 71 (6) ◽  
pp. 481-485 ◽  
Author(s):  
S.M. Amirfakhrian
Keyword(s):  
Magnetic Field ◽  
Numerical Method ◽  
Uncertainty Principle ◽  
Gordon Equation ◽  
Minimal Length ◽  
Spinless Particle ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractIn this article, we studied the Klein–Gordon equation in a generalised uncertainty principle (GUP) framework which predicts a minimal uncertainty in position. We considered a spinless particle in this framework in the presence of a magnetic field, applied in the z-direction, which varies as ${1 \over {{x^2}}}.$ We found the energy eigenvalues of this system and also obtained the correspounding eigenfunctions, using the numerical method. When GUP parameter tends to zero, our solutions were in agreement with those obtained in the absence of GUP.

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