Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0510117

On de Broglie's soliton wave function of many particles with finite masses, energies and momenta

Agus Budiyono

Published Oct 15, 2005• 0 citations
arXivHTMLPDF

Abstract

We consider a mass-less manifestly covariant {\it linear} Schrödinger 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 Schrödinger equation allows one to construct many solitons solution through superposition, each describing a particle with various masses, energies and momenta.

DOI
10.48550/arxiv.quant-ph/0510117

Related papers

On de Broglie's quantum particle as the soliton solution of linear Schrödinger equation

Agus Budiyono

We develop a class of soliton solution of {\it linear} Schrödinger equation without external potential. The quantum probability density generates its own boundary inside which there is internal vibration whose wave number is determined by the velocity of the particle as firstly conjectured by de Broglie. Assuming resonance of the internal vibration will lead to quantization of particle's momentum in term of wave number of the envelope quantum probability density. We further show that the linearity of the Schrödinger equation allows us to have non-interacting many solitons solution through superposition, each describing a particle with equal mass.

arXiv:0704.1726•Apr 13, 2007•0 citations

The Schrodinger Equation only Describes Approximately the Properties of Motion of Microscopic Particles in Quantum Mechanics

Pang Xiao‐feng

Abstract-- We used a nonlinear Schrodinger equation to replace the linear Schrodinger equation and to study further the natures and states of microscopic particles due to plenty of difficulties of quantum mechanics. From this investigation we find that the states and properties of microscopic particles are considerably changed relative to those in quantum mechanics. An outstanding and obvious change is that the microscopic particles have a wave-corpuscle duality in such a case. The solution of the nonlinear Schrodinger equation contains an envelop and carrier waves with determinant frequency which can propagation in medium in a certain velocity. These display the wave feature of particle. However the solutions have all a mass centre and possess a determinant size and mass, momentum and energy, which satisfy also the conservation laws of mass, momentum and energy, at the same time, they meet the collision law of classical particles. These embody the corpuscle feature of the microscopic particles. Finally we seek the reasons and roots generating these changes, which are due to the nonlinear interactions among the particles or between the particles and background field to be considered in the nonlinear Schrodinger equation. The nonlinear interactions provide a double-well potential to make the microscopic particle to be localized as a soliton, and break also through the fundamental hypothesis for the independence of Hamiltonian

•Jan 1, 2008•3 citations

Big crash of basic concepts of physics of the 20th century

Peter Sujak

This paper analyzes the quantities of energy and momentum in the definitional rela-tionship of relativistic mechanics, in the de Broglie momentum hypothesis and in the Klein-Gordon, Dirac and Schrodinger equation. The results of analysis shows that Planck constant and relativistic relationships on the length contraction and increase in mass are a reflection of the same physical principles in nature, that λ designated in the de Broglie hypothesis λ =h/mv as the wave of matter with rest state value λ = ∞ must be connected with a real dimension of a particle with rest state value λ = lo = moc and that on this ba-sis we can come to the fundamental equations of quantum mechanics that are the Klein-Gordon, Dirac and Schrodinger equation without the necessity of the wave functions.

•Aug 1, 2011•5 citations

On the wave-particle-like solutions of nonlinear equations

A. O. Barut, Petre Rusu

The problem of interpreting moving soliton solutions of some nonlinear equations as quantum-like particles is critically analyzed. Purely classical equations (sine-Gordon) as well as nonlinear quantum equations (Schrödinger, Dirac, Kelin–Gordon) are investigated. Three different definitions of energy associated with these equations are considered, and the functional relations replacing the de Broglie postulate, [Formula: see text], are explicitly given. Our analysis shows that fundamental problems generated by the nonlinear approach to quantum mechanics are still unsolved, and these theories have to be considered cautiously.

Canadian Journal of Physics•Feb 1, 1989•3 citations

Planck-Einstein-de Broglie type relations for the acoustic waves

Ion Simaciu, Zoltan Borsos, Gheorghe Dumitrescu +1 more

In this paper we prove, by expressing the energy as a function of the wave propagation speed, it is highlighted the existence of an equivalent mass of the wave, as well as of an Einstein type relations between the energy and this mass. Also, we establish a relation between angular frequency and energy similar to that of the Planck relation. For the propagating wave, there is a de Broglie type relationship between the linear momentum and the action variable (the angular momentum), i.e. the wave linear momentum is proportional to the wave number, the proportionality coefficient being the action.

arXiv:1610.05611•Oct 6, 2016•2 citations

A Soliton Model of the Electron with an internal Nonlinearity cancelling the de Broglie-Bohm Quantum Potential

Roald Ekholdt

The paper proposes an envelope soliton model of the electron that propagates as a protuberance on a fictitious waveguide, which acts as trajectory. The model is based on de Broglie's original electron wave-particle relativistic theory, and on the observation that the Klein-Gordon equation governs the propagation mode of a common microwave waveguide - with the Schroedinger equation as a low group velocity approximation. This analogy opened for practical physical models, including solitons. In the linear case a conceived corpuscle zigzags within the fictitious waveguide - a zigzagging that resembles Penrose's picture of Dirac's electron theory. The soliton envelope is defined by a special nonlinear version of the Schroedinger equation. The nonlinearity cancels the de Broglie/Bohm Quantum Potential of the envelope. The wavefunction is confined by the envelope, and thus the concept of the collapse of the wavefunction is eliminated. Since the electron model is based directly on the Special theory of relativity it also illustrates that theory. The corpuscle, incorporating spin and charge, which moves at the speed of light, needs further study relating it to the photon. A model of the photon based on the mutual coupling of two modes of an optical fiber at the Planck scale, is suggested. One of these modes is thought to carry two orthogonal polarized electromagnetic external fields, while the other, internal, mode carries a corpuscle that moves helically and thus represents the spin. A single electron is considered to have one polarization only, without any superposition possibility; hence, the concept of collapse in a polarization measurement is eliminated.

arXiv:0906.0598•Jun 2, 2009•1 citation
We consider a mass-less manifestly covariant {\it linear} Schrödinger 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 Schrödinger equation allows one to construct many solitons solution through superposition, each describing a particle with various masses, energies and momenta.
We develop a class of soliton solution of {\it linear} Schrödinger equation without external potential. The quantum probability density generates its own boundary inside which there is internal vibration whose wave number is determined by the velocity of the particle as firstly conjectured by de Broglie. Assuming resonance of the internal vibration will lead to quantization of particle's momentum in term of wave number of the envelope quantum probability density. We further show that the linearity of the Schrödinger equation allows us to have non-interacting many solitons solution through superposition, each describing a particle with equal mass.
Abstract-- We used a nonlinear Schrodinger equation to replace the linear Schrodinger equation and to study further the natures and states of microscopic particles due to plenty of difficulties of quantum mechanics. From this investigation we find that the states and properties of microscopic particles are considerably changed relative to those in quantum mechanics. An outstanding and obvious change is that the microscopic particles have a wave-corpuscle duality in such a case. The solution of the nonlinear Schrodinger equation contains an envelop and carrier waves with determinant frequency which can propagation in medium in a certain velocity. These display the wave feature of particle. However the solutions have all a mass centre and possess a determinant size and mass, momentum and energy, which satisfy also the conservation laws of mass, momentum and energy, at the same time, they meet the collision law of classical particles. These embody the corpuscle feature of the microscopic particles. Finally we seek the reasons and roots generating these changes, which are due to the nonlinear interactions among the particles or between the particles and background field to be considered in the nonlinear Schrodinger equation. The nonlinear interactions provide a double-well potential to make the microscopic particle to be localized as a soliton, and break also through the fundamental hypothesis for the independence of Hamiltonian
This paper analyzes the quantities of energy and momentum in the definitional rela-tionship of relativistic mechanics, in the de Broglie momentum hypothesis and in the Klein-Gordon, Dirac and Schrodinger equation. The results of analysis shows that Planck constant and relativistic relationships on the length contraction and increase in mass are a reflection of the same physical principles in nature, that λ designated in the de Broglie hypothesis λ =h/mv as the wave of matter with rest state value λ = ∞ must be connected with a real dimension of a particle with rest state value λ = lo = moc and that on this ba-sis we can come to the fundamental equations of quantum mechanics that are the Klein-Gordon, Dirac and Schrodinger equation without the necessity of the wave functions.
The problem of interpreting moving soliton solutions of some nonlinear equations as quantum-like particles is critically analyzed. Purely classical equations (sine-Gordon) as well as nonlinear quantum equations (Schrödinger, Dirac, Kelin–Gordon) are investigated. Three different definitions of energy associated with these equations are considered, and the functional relations replacing the de Broglie postulate, [Formula: see text], are explicitly given. Our analysis shows that fundamental problems generated by the nonlinear approach to quantum mechanics are still unsolved, and these theories have to be considered cautiously.
In this paper we prove, by expressing the energy as a function of the wave propagation speed, it is highlighted the existence of an equivalent mass of the wave, as well as of an Einstein type relations between the energy and this mass. Also, we establish a relation between angular frequency and energy similar to that of the Planck relation. For the propagating wave, there is a de Broglie type relationship between the linear momentum and the action variable (the angular momentum), i.e. the wave linear momentum is proportional to the wave number, the proportionality coefficient being the action.
The paper proposes an envelope soliton model of the electron that propagates as a protuberance on a fictitious waveguide, which acts as trajectory. The model is based on de Broglie's original electron wave-particle relativistic theory, and on the observation that the Klein-Gordon equation governs the propagation mode of a common microwave waveguide - with the Schroedinger equation as a low group velocity approximation. This analogy opened for practical physical models, including solitons. In the linear case a conceived corpuscle zigzags within the fictitious waveguide - a zigzagging that resembles Penrose's picture of Dirac's electron theory. The soliton envelope is defined by a special nonlinear version of the Schroedinger equation. The nonlinearity cancels the de Broglie/Bohm Quantum Potential of the envelope. The wavefunction is confined by the envelope, and thus the concept of the collapse of the wavefunction is eliminated. Since the electron model is based directly on the Special theory of relativity it also illustrates that theory. The corpuscle, incorporating spin and charge, which moves at the speed of light, needs further study relating it to the photon. A model of the photon based on the mutual coupling of two modes of an optical fiber at the Planck scale, is suggested. One of these modes is thought to carry two orthogonal polarized electromagnetic external fields, while the other, internal, mode carries a corpuscle that moves helically and thus represents the spin. A single electron is considered to have one polarization only, without any superposition possibility; hence, the concept of collapse in a polarization measurement is eliminated.