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

Indian Journal of Advanced Physics

Redefinition of De-Broglie Wavelength Associated with Material Particle

Chandra Bahadur Khadka

Published Feb 10, 2022• 6 citations
Publisher

Abstract

The objective of the work is to reveal the Association of special theory of relativity with De-Broglie wavelength of a particle. It shows that wave nature of a particle is always associated with it’s relativistic properties. The phenomena of interference, diffraction and polarization of light can only be explained on the basis of wave theory of light. These phenomena show that light possesses wave nature. However, certain phenomena like photoelectric effect, Compton effect and discrete emission and absorption of radiation can only be explained on the basis of quantum theory. According to this theory , light propagates in a small packets or quanta and behave like corpuscles or particle. This shows that light possesses particle nature. thus, we can say that light possesses dual nature. The matter also possesses the same dual nature. In order to have wave nature, the particle must satisfy the equation Where m denotes the mass of particle when it is moving with certain velocity. h=6.62×10-34 is the plank’s constant. C is the velocity of light in free space. This shows that wavelength of a material Particle depends on mass. When mathematical operation is done on above equation, it give complete quantitative properties about the wave nature of a particle.

DOI
10.54105/ijap.c1020.041322

Related papers

Derivation of the Missing Equations of Special Relativity from de-Broglie’s Matter Wave Concept and the Correspondence between Them

M.O.G. Talukder, Mushfiq Ahmad

In this paper, we have considered that the particle velocity in the matter wave concept of de Broglie is relative. It reveals that matter wave associated with a moving particle is a photon wave which has longitudinal and transverse values. The conventional de-Broglie’s wavelength-momentum relation corresponds to the longitudinal wave. As a consequence, we have found the longitudinal and transverse relative values of the mass, time, length and velocity including the missing equations of Einstein’s theory of special relativity. It also reveals that momentum and energy are relative quantities and the corresponding expressions for the longitudinal and transverse values for both of them have been presented. Moreover, the addition rules, with a general expression, for all the relative quantities based on Lorentz-Einstein transformation law for the addition of velocities have been given. Finally, the maximum and minimum values of the relative quantities have been expressed in terms of Plank’s constant and the speed of light. Their numerical values have also been calculated and presented in this paper.

Asian Journal of Applied Science and Engineering•Apr 19, 2013•0 citations

Wave-Particle Duality and Electron Kinetic Energy in Quantum Physics and Nanoelectronics

Baldo Alberto Luigi Dalporto, Sabine Mary, Santiago Gallur Santorum

Wave-particle duality is widely regarded as one of the conceptual pillars of modern quantum theory, providing the framework through which the behavior of microscopic matter can be consistently interpreted. According to this principle, microscopic entities such as electrons, photons, atoms and even complex molecules exhibit both wave-like and particle-like properties depending on the experimental configuration used to observe them. This duality is quantitatively formalized through the De Broglie relation, which associates a wavelength with any particle possessing momentum. The present work provides a comprehensive theoretical analysis of the physical and mathematical foundations of wave-particle duality, focusing particularly on the De Broglie wavelength and the kinetic energy of the electron in both non-relativistic and relativistic regimes. The connection between the De Broglie hypothesis and Schrödinger’s equation is discussed in detail, highlighting the role of the kinetic energy operator and the interpretation of matter waves in terms of quantum wave packets. Experimental evidence supporting the wave nature of matter, including electron diffraction experiments and interferometry techniques, is also reviewed. Beyond their conceptual importance, these principles underpin several modern technologies, including electron microscopy, nanoscale semiconductor devices and quantum metrology. The analysis demonstrates that the De Broglie relation provides a unifying framework connecting momentum, wavelength and kinetic energy, thereby forming a fundamental bridge between classical mechanics, quantum theory and modern technological applications.

American Journal of Physics and Applications•Oct 26, 2026•0 citations

Duality of Light and Matter

Z. Ficek

Arguments about particles or waves gave way to a recognized need for both particles and waves in the description of radiation. The confusion over particle versus wave properties was resolved by Louis de Broglie. He postulated that since light has a dual wave–particle nature, matter also has this nature. The idea was to perform a diffraction experiment with electrons. An interference pattern was demonstrated not only with electrons, but also with many kinds of material particles like protons and neutrons. However, any attempt to observe an interference pattern with neutral atoms was found difficult by the fact that atoms carried no charge as electrons do and could not penetrate through condensate matter like neutrons. The de Broglie wavelength of an electron in the smallest orbit turns out to be exactly equal to the circumference of the orbit predicted by Bohr. The interpretation of the interference phenomenon becomes more subtle when the light beams are replaced by individual photons or particles.

•Mar 3, 2017•0 citations

Wave Packet and de Broglie's Wave-particle Duality

Caio Lima Firme

This chapter presents the double-slit experiment and Davisson-Germer’s corresponding experiment that proved the wave-like nature of the electron in 1927. Next, it shows the basics of the special theory of relativity which is used by de Broglie to obtain the wave-particle duality. Afterwards, it displays the most important properties of a periodic wave along with the concepts of travelling wave, composite wave, group velocity, wave packet and single wave packet. These sections are the basis for understanding the de Broglie’s work where he used the special theory of relativity, Einstein’s quantum theory of light and the features of the periodic waves to obtain his famous constant relation of the product of linear momentum (of a particle) and wavelength (of a wave) which became the most important quantum concept used by Schrödinger to develop the quantum wave theory. In the end, a do-it-yourself activity is also given in order to plot several wave packets. (153 words).

CRC Press eBooks•Mar 21, 2022•0 citations

Newton’s Theory of Light and Wave-Particle Duality

Robert J. Buenker

The long history of the dispute among physicists as to whether matter is composed of particles or waves is reviewed. A turning point came at the dawn of the 20th century in the form of the de Broglie momentum-wavelength and Bohr/Planck energy frequency relations. It was on this basis that Schrödinger developed a quantum mechanical differential equation whose solution came to be known as a wave function. The Born Interpretation of these functions holds that their absolute square constitutes a probability distribution which has been used successfully to make predictions of the properties of the system under discussion. It is pointed out that the phenomenon of light refraction played a key role in the development of both Newton’s corpuscular theory of light and the competing theory of Huygens which looks upon light as consisting exclusively of waves. It is shown that Newton’s failure to predict the decrease in the speed of light as it passes from air into water was not because of his belief in the particle composition of light, but rather because he not did anticipate that the mass of a photon changes upon entering a medium of higher index of refraction n. By assuming that the energy E of light is equal pc/n, where p is the momentum of the photons and c is the speed of light in free space, it is shown that the experimental dependence of the speed the light on its wavelength as it passes through a transparent medium is derived successfully through the use of Hamilton’s Canonical Equations and Newton’s Second Law of Kinetics. It is suggested that the relationship between particles and waves can be understood by noting that the localized properties of matter exhibit themselves in experiments such as the photoelectric effect where attention can be concentrated on the behavior of a single particle. The corresponding wave properties occur when large numbers of particles are observed under exactly similar circumstances, as for example in electron diffraction. ...........

East African Scholars Journal of Engineering and Computer Sciences•May 15, 2022•1 citation

The Photon as a Mass Particle Associated with a Wave

Adnan Salih Al-Ithawi

Neither the pure wave theory nor the pure particle theory can explain the nature of light. Light must be both a particle and a wave. It is a wave because it exhibits interference effects. At the same time, the fact that the photographs contain discrete dots is a direct demonstration that light refuses to be split into units of less than a single photon. We found a general equations that solved all the problems in the current theories for the photon and explained the nature of light by suggesting new hypotheses. According to our results, the photon is a particle which has mass and associated with a wave. The results of the research proved that the refractive index of materials varies with the natural mass of the photon.

International journal of optics and applications•Jan 1, 2015•7 citations
The objective of the work is to reveal the Association of special theory of relativity with De-Broglie wavelength of a particle. It shows that wave nature of a particle is always associated with it’s relativistic properties. The phenomena of interference, diffraction and polarization of light can only be explained on the basis of wave theory of light. These phenomena show that light possesses wave nature. However, certain phenomena like photoelectric effect, Compton effect and discrete emission and absorption of radiation can only be explained on the basis of quantum theory. According to this theory , light propagates in a small packets or quanta and behave like corpuscles or particle. This shows that light possesses particle nature. thus, we can say that light possesses dual nature. The matter also possesses the same dual nature. In order to have wave nature, the particle must satisfy the equation Where m denotes the mass of particle when it is moving with certain velocity. h=6.62×10-34 is the plank’s constant. C is the velocity of light in free space. This shows that wavelength of a material Particle depends on mass. When mathematical operation is done on above equation, it give complete quantitative properties about the wave nature of a particle.
In this paper, we have considered that the particle velocity in the matter wave concept of de Broglie is relative. It reveals that matter wave associated with a moving particle is a photon wave which has longitudinal and transverse values. The conventional de-Broglie’s wavelength-momentum relation corresponds to the longitudinal wave. As a consequence, we have found the longitudinal and transverse relative values of the mass, time, length and velocity including the missing equations of Einstein’s theory of special relativity. It also reveals that momentum and energy are relative quantities and the corresponding expressions for the longitudinal and transverse values for both of them have been presented. Moreover, the addition rules, with a general expression, for all the relative quantities based on Lorentz-Einstein transformation law for the addition of velocities have been given. Finally, the maximum and minimum values of the relative quantities have been expressed in terms of Plank’s constant and the speed of light. Their numerical values have also been calculated and presented in this paper.
Wave-particle duality is widely regarded as one of the conceptual pillars of modern quantum theory, providing the framework through which the behavior of microscopic matter can be consistently interpreted. According to this principle, microscopic entities such as electrons, photons, atoms and even complex molecules exhibit both wave-like and particle-like properties depending on the experimental configuration used to observe them. This duality is quantitatively formalized through the De Broglie relation, which associates a wavelength with any particle possessing momentum. The present work provides a comprehensive theoretical analysis of the physical and mathematical foundations of wave-particle duality, focusing particularly on the De Broglie wavelength and the kinetic energy of the electron in both non-relativistic and relativistic regimes. The connection between the De Broglie hypothesis and Schrödinger’s equation is discussed in detail, highlighting the role of the kinetic energy operator and the interpretation of matter waves in terms of quantum wave packets. Experimental evidence supporting the wave nature of matter, including electron diffraction experiments and interferometry techniques, is also reviewed. Beyond their conceptual importance, these principles underpin several modern technologies, including electron microscopy, nanoscale semiconductor devices and quantum metrology. The analysis demonstrates that the De Broglie relation provides a unifying framework connecting momentum, wavelength and kinetic energy, thereby forming a fundamental bridge between classical mechanics, quantum theory and modern technological applications.
Arguments about particles or waves gave way to a recognized need for both particles and waves in the description of radiation. The confusion over particle versus wave properties was resolved by Louis de Broglie. He postulated that since light has a dual wave–particle nature, matter also has this nature. The idea was to perform a diffraction experiment with electrons. An interference pattern was demonstrated not only with electrons, but also with many kinds of material particles like protons and neutrons. However, any attempt to observe an interference pattern with neutral atoms was found difficult by the fact that atoms carried no charge as electrons do and could not penetrate through condensate matter like neutrons. The de Broglie wavelength of an electron in the smallest orbit turns out to be exactly equal to the circumference of the orbit predicted by Bohr. The interpretation of the interference phenomenon becomes more subtle when the light beams are replaced by individual photons or particles.
This chapter presents the double-slit experiment and Davisson-Germer’s corresponding experiment that proved the wave-like nature of the electron in 1927. Next, it shows the basics of the special theory of relativity which is used by de Broglie to obtain the wave-particle duality. Afterwards, it displays the most important properties of a periodic wave along with the concepts of travelling wave, composite wave, group velocity, wave packet and single wave packet. These sections are the basis for understanding the de Broglie’s work where he used the special theory of relativity, Einstein’s quantum theory of light and the features of the periodic waves to obtain his famous constant relation of the product of linear momentum (of a particle) and wavelength (of a wave) which became the most important quantum concept used by Schrödinger to develop the quantum wave theory. In the end, a do-it-yourself activity is also given in order to plot several wave packets. (153 words).
The long history of the dispute among physicists as to whether matter is composed of particles or waves is reviewed. A turning point came at the dawn of the 20th century in the form of the de Broglie momentum-wavelength and Bohr/Planck energy frequency relations. It was on this basis that Schrödinger developed a quantum mechanical differential equation whose solution came to be known as a wave function. The Born Interpretation of these functions holds that their absolute square constitutes a probability distribution which has been used successfully to make predictions of the properties of the system under discussion. It is pointed out that the phenomenon of light refraction played a key role in the development of both Newton’s corpuscular theory of light and the competing theory of Huygens which looks upon light as consisting exclusively of waves. It is shown that Newton’s failure to predict the decrease in the speed of light as it passes from air into water was not because of his belief in the particle composition of light, but rather because he not did anticipate that the mass of a photon changes upon entering a medium of higher index of refraction n. By assuming that the energy E of light is equal pc/n, where p is the momentum of the photons and c is the speed of light in free space, it is shown that the experimental dependence of the speed the light on its wavelength as it passes through a transparent medium is derived successfully through the use of Hamilton’s Canonical Equations and Newton’s Second Law of Kinetics. It is suggested that the relationship between particles and waves can be understood by noting that the localized properties of matter exhibit themselves in experiments such as the photoelectric effect where attention can be concentrated on the behavior of a single particle. The corresponding wave properties occur when large numbers of particles are observed under exactly similar circumstances, as for example in electron diffraction. ...........
Neither the pure wave theory nor the pure particle theory can explain the nature of light. Light must be both a particle and a wave. It is a wave because it exhibits interference effects. At the same time, the fact that the photographs contain discrete dots is a direct demonstration that light refuses to be split into units of less than a single photon. We found a general equations that solved all the problems in the current theories for the photon and explained the nature of light by suggesting new hypotheses. According to our results, the photon is a particle which has mass and associated with a wave. The results of the research proved that the refractive index of materials varies with the natural mass of the photon.