By inference,this paper expounds that the relation of de Broglie wave's speed,length and frequency differs from that of classical waves such as mechanical wave and electromagnenic wave,and its wavelength and frequency do not have the physical meanings described by the classical theory.The reason is that de Broglie wave is not a simple representation of the classical wave,and the meanings of particle and volatility are special in wave-particle dualism.
By inference,this paper expounds that the relation of de Broglie wave's speed,length and frequency differs from that of classical waves such as mechanical wave and electromagnenic wave,and its wavelength and frequency do not have the physical meanings described by the classical theory.The reason is that de Broglie wave is not a simple representation of the classical wave,and the meanings of particle and volatility are special in wave-particle dualism.
This article proposes a conceptual analysis of the reasoning developed by Louis de Broglie in his 1924 thesis Recherches sur la théorie des quanta, particularly the pages devoted to the derivation of the phase wave. By distinguishing the proper frequency associated with the particle at rest, the frequency observed from the stationary frame, and the frequency derived from the relativistic energy of the corpuscle, we show that these different frequencies do not appear to possess the same physical status in de Broglie’s original reasoning. We therefore examine the hypothesis according to which the introduction of the phase wave primarily responds to the necessity of maintaining relativistic coherence between two distinct interpretations of frequency. This study does not challenge the physical validity of the de Broglie relation linking momentum and wavelength, but rather proposes a critical re-examination of the conceptual status of the frequencies involved in the original 1924 construction. Finally, we discuss the possibility of future geometrical or topological reformulations of this relation without explicit recourse to a superluminal hase wave.
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.
The velocity is a macroscopic concept. The question what is the meaning of velocity in Quantum Mechanics( QM) ,this problem itself is inno answersituation. In the semi-classical theory,for the reconstruction of the velocity definition,we have v→= ▽S / m[m is the particle's mass and ψ = Aexp( j S /h) ]. This method builds the relation of velocity and wave function,but it is not the necessary and useful concept of wave's speed. The velocity of light in vacuum is a common basic constant of physics,however QM also need this parameter obviously,i. e. the new wave mechanics is on need of this physical quantity.The process and result of people's practice show that,scientist has intended to bring forth in the measurement of c with very high accuracy does stand out,if he used the scalar equation c = fλ. Modern physics maintain that the wave velocities( phase velocityvp、group velocity vg) are scalars,not vectors.The wave has its special scientific features; the regular pattern is different from the Classical Mechanics( CM). It needs supports of the QM,but it is not identical with the serious QM. Now,it has not only a theory that can explain the wave problems perfectly,so it is support by the classical physics and quantum physics.The quantization process of EM fields explains the particle-wave duality mathematically. Post quantization,from the EM fields we obtained the photons. But scientist still is puzzled by a difficult question:what is photon. As the common knowledge,the matter waves of photon still a paradox in physics. In addition,the electronic probability waves corresponding the Schrdinger equation,but people says the photonic probability waves have not that wave equation. In other words,the physical meanings of matter wave's phase velocity are not clear,and why the phase velocity of de Broglie waves is faster-than-light,many explanations will be needed.Many instances similar to these examples make the particle-wave duality still the magic ghost in modern physics. Finally,the study on negative wave velocity( NWV) in recent years has a great deal of experience on wave sciences,and bring the new chance on theoretical thinking.
Abstract Properties of de Broglie waves and their differences from any other waves, for example, electromagnetic, are discussed. Their little-known properties are given: 1) the propagation velocity is greater than the speed of light V > c ; 2) dispersion even in vacuum (waves of different frequencies propagate at different speeds, which results in the spreading of any wave packets associated with the particles); 3) the connection of the de Broglie wave with another physical wave moving with a speed v less than the speed of light, but so always v · V = c 2, and for the photons v = V = c. According to later views of de Broglie, this second wave is not the group wave. Possible mechanisms of generating the de Broglie waves based on spherical and cylindrical hollow quantum resonators, which can be specially created in matter using specific nanostructures are considered. Perhaps their nature itself realizes them for any micro-objects, regardless of their electrical, magnetic and gravitational properties. That is, this phenomenon is universal. Applications and realizations of this idea are discussed in the part II of our article.
In this article, it is shown that if a particle is at rest and has some harmonic oscillation, then a traveling particle with a constant speed corresponds to a De Broglie Wave.In 1924, De Broglie proposed that particles of matter exhibit wave like behavior, the expression for which became fundamental in the creation of wave mechanics (quantum mechanics).The main equation for this is the Schrödinger equation, which in the case of free motion of a particle becomes the expression for the De Broglie wave.This hypothesis is supported by many early experiments on the diffraction of electrons, and later the development of modern physics.However until now, the origin of this hypothesis remains unclear.We show that the expression for the De Broglie wavelength can be obtained from a more general well-known concept, that any particle at rest has a corresponding harmonic oscillation that transforms into a wave of a moving particle with the help of relativistic change of coordinates (the Lorentz transformations).In this way, a De Broglie wave can be explained as a spacetime wave.