scholarly journals Wave Equation of a Particle with the Exponential Hamiltonian in the Gravitational and Electromagnetic Field

2019 ◽  
Vol 5 (3) ◽  
Author(s):  
N. Perković ◽  
M. Stojić
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation

scholarly journals Some arguments for the wave equation in Quantum theory

2021 ◽  
Vol 5 (1) ◽  
pp. 314-336
Author(s):  
Tristram de Piro ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Continuity Equation ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Atomic System ◽  
Balmer Series ◽  
Inertial Frames ◽  
The Stability

We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.

Singularities of electron kernel functions in an external electromagnetic field

1954 ◽  
Vol 222 (1148) ◽  
pp. 93-108 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Wave Equation ◽  
Vacuum Polarization ◽  
Proper Time ◽  
External Electromagnetic Field ◽  
Kernel Functions ◽  
Second Order ◽  
Significant Part ◽  
Second Order Wave Equation

The electron kernel functions are derived from solutions of the second-order wave equation, using the proper-time parametrization. Iterated kernel functions are introduced and a gauge-independent perturbation theory is developed. The separation of singular parts proceeds in terms of the iterated kernel functions valid in the absence of an electromagnetic field, and the singular expressions which have to be compensated in order to determine the physically significant part of the vacuum polarization are obtained in a more transparent form than those given originally by Heisenberg.

scholarly journals Some applications of the Riesz potential to the theory of the electromagnetic field and the meson field

1946 ◽  
Vol 188 (1012) ◽  
pp. 18-31 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Differential Equations ◽  
Riesz Potential ◽  
Analytical Continuation ◽  
Neutral Meson ◽  
Meson Field ◽  
Hyperbolic Differential Equations ◽  
Proper Energy

This paper contains some applications of the method of Marcel Riesz in the solution of normal hyperbolic differential equations, in particular the wave equation, where the known difficulties, due to the occurrence of divergent integrals, are avoided by a process of analytical continuation. In the theory of the electromagnetic field the method yields simple deductions of classical results, but also the results recently obtained by Dirac regarding the proper energy and proper momentum of an electron are obtained without any addition of new assumptions. The corresponding problem in Bhabha’s analogous theory for the neutral meson field are also studied.

scholarly journals The Dual Continuity Equations

2018 ◽  
Author(s):  
Arbab Arbab ◽  
Norah N. Alsaawi
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Gauge Invariance ◽  
Maxwell Equations ◽  
Continuity Equation ◽  
Mathematical Structure ◽  
Magnetic Monopoles ◽  
System Of Equations ◽  
Duality Transformation ◽  
Continuity Equations

The ordinary continuity equation relating the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The horizontal and transverse currents and the densities associated with them are found to be coupled to each other. Each of these quantities are found to obey a wave equation traveling at the velocity of light in vacuum. London's equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London's equations are symmetric and are shown to be dual to each other. It is shown that London's equations are Maxwell's equations with massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

Propagation of two-dimensional extremely short optical pulses in photonic crystal with silicene

2019 ◽  
Vol 33 (04) ◽  
pp. 1950037
Author(s):  
Natalia N. Konobeeva ◽  
Mikhail B. Belonenko
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Photonic Crystal ◽  
Electromagnetic Pulse ◽  
Two Dimensional ◽  
Initial Amplitude ◽  
Optical Pulses ◽  
Extremely Short Optical Pulses

We consider the wave equation for an electromagnetic field propagating in silicene placed in photonic crystal (PC). We study the effects observed when the depth of the nonlinearity modulation are varied, as well as the initial amplitude of the electromagnetic pulse.

Spinor Wave Equation of Electromagnetic Field

2013 ◽  
Vol 53 (3) ◽  
pp. 1010-1021
Author(s):  
Xiang-Yao Wu ◽  
Hong Li ◽  
Xiao-Jing Liu ◽  
Bo-Jun Zhang ◽  
Jing-Hai Yang ◽  
...  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Spinor Wave

RELATIVISTIC PARTICLE WITH CURVATURE IN AN EXTERNAL ELECTROMAGNETIC FIELD

1991 ◽  
Vol 06 (22) ◽  
pp. 3989-3996 ◽  
Author(s):  
V.V. NESTERENKO
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Phase Space ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Canonical Quantization ◽  
Hamiltonian Formalism ◽  
External Electromagnetic Field ◽  
Operator Form ◽  
Complete Set

A model of a relativistic particle with curvature interacting with an external electromagnetic field in a “minimal way” is investigated. The generalized Hamiltonian formalism for this model is constructed. A complete set of the constraints in the phase space is obtained and then divided into first- and second-class constraints. On this basis the canonical quantization of the model is considered. A wave equation in the operator form, resembling the Dirac equation in an external electromagnetic field, is obtained. The massless version of this model is briefly discussed.

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