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.

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.

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.

FRACTIONAL ANALYSIS OF WAVE PACKET PROPAGATION AND SOME ASPECTS OF VSL WITH GUP

Fractals ◽  
2008 ◽  
Vol 16 (01) ◽  
pp. 33-42 ◽  
Author(s):  
S. HAMID MEHDIPOUR ◽  
KOUROSH NOZARI ◽  
S. DAVOOD SADATIAN
Keyword(s):  
Wave Packet ◽  
Gordon Equation ◽  
Generalized Uncertainty Principle ◽  
De Sitter ◽  
Modified Dispersion Relation ◽  
Fractional Analysis ◽  
Klein Gordon ◽  
De Sitter Universe ◽  
Klein Gordon Equation ◽  
Wave Packet Broadening

In this paper, we consider the problem of wave packet broadening in the framework of the Generalized Uncertainty Principle (GUP) of quantum gravity. Then we find a fractal Klein-Gordon equation to further analyze the wave packet broadening in a foamy spacetime. We derive a Modified Dispersion Relation (MDR) in the context of GUP which shows an extra broadening due to gravitational induced uncertainty. As a result of these dispersion relations, a generalized Klein-Gordon equation can be obtained. We solve this generalized equation under certain conditions to find both analytical and numerical results. We show that GUP can lead to a variation of the fundamental constants such as speed of light. With this novel properties, we find a time-dependent equation of state for perfect fluid in de Sitter universe and we interpret its physical implications.

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.

Sign in / Sign up

Export Citation Format

Share Document