dorsal/arxiv
View SchemaDeveloping de Broglie Wave
| Authors | J X Zheng-Johansson, P-I Johansson |
|---|---|
| Categories | |
| ArXiv ID | physics/0608265 |
| URL | https://arxiv.org/abs/physics/0608265 |
| Journal | In: Prog. in Physics, v.4, 32-35, 2006; excerpt from: J.X. Zheng-Johansson and P-I. Johansson, Unification of Classical, Quantum and Relativistic Mechanics and of the Four Forces, Nova Sci. Pub., 2nd print., later 2006 |
Abstract
The electromagnetic component waves, comprising together with their generating oscillatory massless charge a material particle, will be Doppler shifted when the charge hence particle is in motion, with a velocity $v$, as a mere mechanical consequence of the source motion. We illustrate here that two such component waves generated in opposite directions and propagating at speed $c$ between walls in a one-dimensional box, superpose into a traveling beat wave of wavelength ${\mit\Lambda}_d$$=(\frac{v}{c}){\mit\Lambda}$ and phase velocity $c^2/v+v$ which resembles directly L. de Broglie's hypothetic phase wave. This phase wave in terms of transporting the particle mass at the speed $v$ and angular frequency ${\mit\Omega}_d=2\pi v /{\mit\Lambda}_d$, with ${\mit\Lambda}_d$ and ${\mit\Omega}_d$ obeying the de Broglie relations, represents a de Broglie wave. The standing-wave function of the de Broglie (phase) wave and its variables for particle dynamics in small geometries are equivalent to the eigen-state solutions to Schr\"odinger equation of an identical system.
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"abstract": "The electromagnetic component waves, comprising together with their\ngenerating oscillatory massless charge a material particle, will be Doppler\nshifted when the charge hence particle is in motion, with a velocity $v$, as a\nmere mechanical consequence of the source motion. We illustrate here that two\nsuch component waves generated in opposite directions and propagating at speed\n$c$ between walls in a one-dimensional box, superpose into a traveling beat\nwave of wavelength ${\\mit\\Lambda}_d$$=(\\frac{v}{c}){\\mit\\Lambda}$ and phase\nvelocity $c^2/v+v$ which resembles directly L. de Broglie\u0027s hypothetic phase\nwave. This phase wave in terms of transporting the particle mass at the speed\n$v$ and angular frequency ${\\mit\\Omega}_d=2\\pi v /{\\mit\\Lambda}_d$, with\n${\\mit\\Lambda}_d$ and ${\\mit\\Omega}_d$ obeying the de Broglie relations,\nrepresents a de Broglie wave. The standing-wave function of the de Broglie\n(phase) wave and its variables for particle dynamics in small geometries are\nequivalent to the eigen-state solutions to Schr\\\"odinger equation of an\nidentical system.",
"arxiv_id": "physics/0608265",
"authors": [
"J X Zheng-Johansson",
"P-I Johansson"
],
"categories": [
"physics.gen-ph"
],
"journal_ref": "In: Prog. in Physics, v.4, 32-35, 2006; excerpt from: J.X.\n Zheng-Johansson and P-I. Johansson, Unification of Classical, Quantum and\n Relativistic Mechanics and of the Four Forces, Nova Sci. Pub., 2nd print.,\n later 2006",
"title": "Developing de Broglie Wave",
"url": "https://arxiv.org/abs/physics/0608265"
},
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