dorsal/arxiv
View SchemaOn de Broglie's soliton wave function of many particles with finite masses, energies and momenta
| Authors | Agung Budiyono |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510117 |
| URL | https://arxiv.org/abs/quant-ph/0510117 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We consider a mass-less manifestly covariant {\it linear} Schr\"odinger equation. First, we show that it possesses a class of non-dispersive soliton solution with finite-size spatio-temporal support inside which the quantum amplitude satisfies the Klein-Gordon equation with finite {\it emergent} mass. We then proceed to interpret the soliton wave function as describing a particle with finite mass, energy and momentum. Inside the spatio-temporal support, the wave function shows spatio-temporal internal vibration with angular frequency and wave number that are determined by the energy-momentum of the particle as firstly conjectured by de Broglie. Imposing resonance of the internal vibration inside the spatio-temporal support leads to Planck-Einstein quantization of energy-momentum. The first resonance mode is shown to recover the classical energy-momentum relation developed in special relativity. We further show that the linearity of the Schr\"odinger equation allows one to construct many solitons solution through superposition, each describing a particle with various masses, energies and momenta.
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"date_created": "2026-03-02T18:02:20.600000Z",
"date_modified": "2026-03-02T18:02:20.600000Z",
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"abstract": "We consider a mass-less manifestly covariant {\\it linear} Schr\\\"odinger\nequation. First, we show that it possesses a class of non-dispersive soliton\nsolution with finite-size spatio-temporal support inside which the quantum\namplitude satisfies the Klein-Gordon equation with finite {\\it emergent} mass.\nWe then proceed to interpret the soliton wave function as describing a particle\nwith finite mass, energy and momentum. Inside the spatio-temporal support, the\nwave function shows spatio-temporal internal vibration with angular frequency\nand wave number that are determined by the energy-momentum of the particle as\nfirstly conjectured by de Broglie. Imposing resonance of the internal vibration\ninside the spatio-temporal support leads to Planck-Einstein quantization of\nenergy-momentum. The first resonance mode is shown to recover the classical\nenergy-momentum relation developed in special relativity. We further show that\nthe linearity of the Schr\\\"odinger equation allows one to construct many\nsolitons solution through superposition, each describing a particle with\nvarious masses, energies and momenta.",
"arxiv_id": "quant-ph/0510117",
"authors": [
"Agung Budiyono"
],
"categories": [
"quant-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "On de Broglie\u0027s soliton wave function of many particles with finite masses, energies and momenta",
"url": "https://arxiv.org/abs/quant-ph/0510117"
},
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"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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