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:0901.4241

Towards the demystificatiom of quantum interference

Peter Leifer

Published Jan 27, 2009• 0 citations
arXivHTMLPDF

Abstract

It has been shown that velocity of propagation of wave front cannot coincide with observable velocity of quantum particles. It is additional argument leads to conclusion that phase wave of de Broglie cannot be associated with single "elementary" particle like electron. Therefore quantum interference under linear superposition cannot describe energy distribution in extended quantum particles. Essentially new approach is required in order to establish non-linear relativistic wave equations with soliton-like solutions.

DOI
10.48550/arxiv.0901.4241

Related papers

About the non-relativistic limit of the phase velocity of matter waves

Douglas F. Mundarain

Abstract This work revisits the apparent paradox that emerges from some results found in many basic textbooks which address the problem of calculating the phase velocity of free particles in the relativistic regime and its relation with the same quantity in the non-relativistic regime. Because some books use the Newtonian kinetic energy and others use the total relativistic energy (including the rest energy), the non-relativistic limit of the relativistic phase velocity differs from the Newtonian phase velocity, which can be confusing for many students. This paper proposes expressing the phase velocity by first subtracting the rest energy from the relativistic energy before imposing the usual de Broglie relations. In addition to providing the corresponding Newtonian phase velocity, it also provides a relativistic Schrödinger equation which intuitively reduces to the non-relativistic Schrödinger equation in the appropriate regime. The problem of the equivalence between the relativistic Schrödinger equation and the Klein–Gordon equation is also addressed by using arguments which can be understood by undergraduate students.

European Journal of Physics•Apr 18, 2017•3 citations

The de Broglie Wave as Evidence of a Deeper Wave Structure

Daniel Shanahan

It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically induced modulation of an underlying carrier wave that moves with the velocity of the particle. In the rest frame of the particle this underlying structure has the form of a standing wave. De Broglie also assumed the existence of this antecedent standing wave, but it would appear that he failed to notice its survival as a carrier wave in the Lorentz transformed wave structure. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, evidencing a more natural unity between matter and radiation than might otherwise be contemplated, and avoiding the necessity of recovering the particle velocity from a superposition of such waves. Because the Schrödinger and other wave equations for massive particles were conceived as equations for the de Broglie wave, this interpretation of the wave is also relevant to such issues in quantum mechanics as the meaning of the wave function, the nature of wave-particle duality, and the possibility of well-defined particle trajectories.

arXiv:1503.02534•Mar 6, 2015•0 citations

Interference and Diffraction of Quantum Particles Revisited

T Shivalingaswamy, B. A. Kagali

Interference and diffraction phenomena are the basic properties shown by waves. De-Broglie concept of matter waves brought in the extended version of wave properties of material particles. Wave properties of quantum particles are important to understand various phenomena in physics. Matter waves are a core part of quantum theory. Now wave-particle duality is exploited for many applications such as imaging microscopic particles using electron microscopes etc. Here we deduce the interference and diffraction of quantum particles on the basis of the propagation amplitude according to the path integral formulation of quantum mechanics. The intensity distribution due to interference and diffraction of quantum particles are compared with those obtained from the formal methods. The results agree with the traditional approach assuming a deBroglie wave associated with particles.

Mapana Journal of Sciences•Jul 14, 2023•0 citations

Hopeless Phase Velocity

Rei Beaumanner, Carl-Gustav Hedenby

Among the exciting outcomes of the Beaumanner relative quantum formula RQF is the linking of de Broglie's matter wave length to the velocity of light. I show that a phase velocity introduced by de Broglie is not believable since it comes from relating his matter wave length to the total Einstein energy. Instead it should relate to the energy of mechanical momentum which I have defined. In an additional argument I show that the strange phase velocity also can be viewed as coming from an assumption that mechanical momentum is linearly coupled to the total energy, which it is not.

•Jan 1, 2014•0 citations

On the Nature of Quantum Waves

L. Ellam

Technology majors when introduced to quantum concepts, invariably encounter difficulties in the understanding of matter waves. Further, de Broglie waves are usually considered to be different from the waves inherent in Schrodinger's equation. The purpose of this paper is to clarify the nature of quantum waves and to pursue the implications of wave-particle duality.

International Journal of Bahamian Studies•Dec 20, 2007•0 citations

Generalized guidance equation for peaked quantum solitons: the single particle case

Thomas Durt

We study certain non-linear generalisations of the Schr{ö}dinger equation which admit static solitonic 2 solutions in absence of external potential acting on the particle. We consider a class of solutions that can be written as a product of a solution of the linear Schr{ö}dinger equation with a peaked quantum soliton, in a regime where the size of the soliton is quite smaller than the typical scale of variation of the linear wave. In the non-relativistic limit, the solitons obey a generalized de Broglie-Bohm (dB-B) guidance equation. In first approximation, this guidance equation reduces to the dB-B guidance equation according to which they move at the so-called de Broglie-Bohm velocity along the hydrodynamical flow lines of the linear Schr{ö}dinger wave. If we consider a spinorial electronic wave function a la Dirac, its barycentre is predicted to move exactly in accordance with the dB-B guidance equation.

arXiv:1602.03133•Feb 9, 2016•1 citation
It has been shown that velocity of propagation of wave front cannot coincide with observable velocity of quantum particles. It is additional argument leads to conclusion that phase wave of de Broglie cannot be associated with single "elementary" particle like electron. Therefore quantum interference under linear superposition cannot describe energy distribution in extended quantum particles. Essentially new approach is required in order to establish non-linear relativistic wave equations with soliton-like solutions.
Abstract This work revisits the apparent paradox that emerges from some results found in many basic textbooks which address the problem of calculating the phase velocity of free particles in the relativistic regime and its relation with the same quantity in the non-relativistic regime. Because some books use the Newtonian kinetic energy and others use the total relativistic energy (including the rest energy), the non-relativistic limit of the relativistic phase velocity differs from the Newtonian phase velocity, which can be confusing for many students. This paper proposes expressing the phase velocity by first subtracting the rest energy from the relativistic energy before imposing the usual de Broglie relations. In addition to providing the corresponding Newtonian phase velocity, it also provides a relativistic Schrödinger equation which intuitively reduces to the non-relativistic Schrödinger equation in the appropriate regime. The problem of the equivalence between the relativistic Schrödinger equation and the Klein–Gordon equation is also addressed by using arguments which can be understood by undergraduate students.
It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically induced modulation of an underlying carrier wave that moves with the velocity of the particle. In the rest frame of the particle this underlying structure has the form of a standing wave. De Broglie also assumed the existence of this antecedent standing wave, but it would appear that he failed to notice its survival as a carrier wave in the Lorentz transformed wave structure. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, evidencing a more natural unity between matter and radiation than might otherwise be contemplated, and avoiding the necessity of recovering the particle velocity from a superposition of such waves. Because the Schrödinger and other wave equations for massive particles were conceived as equations for the de Broglie wave, this interpretation of the wave is also relevant to such issues in quantum mechanics as the meaning of the wave function, the nature of wave-particle duality, and the possibility of well-defined particle trajectories.
Interference and diffraction phenomena are the basic properties shown by waves. De-Broglie concept of matter waves brought in the extended version of wave properties of material particles. Wave properties of quantum particles are important to understand various phenomena in physics. Matter waves are a core part of quantum theory. Now wave-particle duality is exploited for many applications such as imaging microscopic particles using electron microscopes etc. Here we deduce the interference and diffraction of quantum particles on the basis of the propagation amplitude according to the path integral formulation of quantum mechanics. The intensity distribution due to interference and diffraction of quantum particles are compared with those obtained from the formal methods. The results agree with the traditional approach assuming a deBroglie wave associated with particles.
Among the exciting outcomes of the Beaumanner relative quantum formula RQF is the linking of de Broglie's matter wave length to the velocity of light. I show that a phase velocity introduced by de Broglie is not believable since it comes from relating his matter wave length to the total Einstein energy. Instead it should relate to the energy of mechanical momentum which I have defined. In an additional argument I show that the strange phase velocity also can be viewed as coming from an assumption that mechanical momentum is linearly coupled to the total energy, which it is not.
We study certain non-linear generalisations of the Schr{ö}dinger equation which admit static solitonic 2 solutions in absence of external potential acting on the particle. We consider a class of solutions that can be written as a product of a solution of the linear Schr{ö}dinger equation with a peaked quantum soliton, in a regime where the size of the soliton is quite smaller than the typical scale of variation of the linear wave. In the non-relativistic limit, the solitons obey a generalized de Broglie-Bohm (dB-B) guidance equation. In first approximation, this guidance equation reduces to the dB-B guidance equation according to which they move at the so-called de Broglie-Bohm velocity along the hydrodynamical flow lines of the linear Schr{ö}dinger wave. If we consider a spinorial electronic wave function a la Dirac, its barycentre is predicted to move exactly in accordance with the dB-B guidance equation.