Solution of the Klein‐Gordon and Dirac Equations for a Particle with a Plane Electromagnetic Wave and a Parallel Magnetic Field

1965 ◽  
Vol 6 (7) ◽  
pp. 1163-1169 ◽  
Author(s):  
Peter J. Redmond
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Plane Electromagnetic Wave ◽  
Parallel Magnetic Field ◽  
Dirac Equations ◽  
Klein Gordon

scholarly journals "Cut wires grating – single longitudinal wire" planar metastructure to achieve microwave magnetic resonance in a single wire

2012 ◽  
Vol 1 (2) ◽  
pp. 16
Author(s):  
G. Kraftmakher ◽  
V. Butylkin
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Plane Electromagnetic Wave ◽  
Experimental Investigations ◽  
Magnetic Response ◽  
Resonant Response ◽  
Single Wire ◽  
Surface Polaritons ◽  
Varactor Diodes ◽  
Wire Grating

Here we present metastructures containing cut-wire grating and a single longitudinal cut-wire orthogonal to grating’s wires. Experimental investigations at microwaves show these structures can provide strong magnetic resonant response of a single nonmagnetic cut-wire in dependence on configuration and sizes in the case when metastructures are oriented along the direction of wave propagation and cut-wires of grating are parallel to the electric field of a plane electromagnetic wave. It is suggested a concept of magnetic response based on antiparallel resonant currents excited by magnetic field of surface polaritons in many spatial LC-circuits created from cut-wire pairs of a grating and section of longitudinal cut-wire. Three separately observed resonant effects connected with grating, LC-circuits and with longitudinal cut-wire have been identified applying measurements in waveguides, cutoff waveguides and free space. To tune and mark resonance split cut-wires are loaded with varactor diodes.

Durchgang von Mikrowellen durch ebene Plasmaschichten

1962 ◽  
Vol 17 (1) ◽  
pp. 59-64
Author(s):  
K. Hain ◽  
M. Tutter
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Static Magnetic Field ◽  
Plane Electromagnetic Wave ◽  
Reflection And Transmission ◽  
Plasma Slab ◽  
Plane Plasma

The reflection and transmission of a plane electromagnetic wave propagating through a plane plasma slab with and without a static magnetic field is computed.

DIFFRACTION BY A CONDUCTING HALF-PLANE IN PLASM

1966 ◽  
Vol 44 (6) ◽  
pp. 1207-1212
Author(s):  
Ll. G. Chambers
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Half Plane ◽  
Field Component ◽  
Plane Electromagnetic Wave ◽  
Static Field ◽  
Anisotropic Plasma ◽  
Magnetic Field Component ◽  
Permittivity Tensor ◽  
Arbitrary Direction

The problem considered is that of a plane electromagnetic wave approaching from an arbitrary direction a perfectly conducting half-plane in an anisotropic plasma, characterized by a permittivity tensor. The system is such that the wave has a single magnetic field component, which is parallel both to the magneto-static field and the diffracting edge. The work is a simplification of previous work by Jull, involving the use of methods previously developed by the author.

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.

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