As for DE Broglie's hypothesis of matter waves, many experimental physicists have experimentally verified it by using cathode ray tube and proved that matter waves do exist, so there is a mysterious hypothesis of wave-particle duality.In this paper, according to the electric field force of electrons in the cathode ray tube and the continuity equation of electrons, Under assumptions such as inelastic approximation, it is proved that the wave-particle duality is actually the macroscopic motion of real particles in the form of waves.In this paper, it is proved theoretically that the component of electron velocity in the tube satisfies the wave equation, and the wave velocity varies with the change of electric potential in the tube.From the discussion in this paper, it can be seen that there are still some problems to be studied about the motion of electrons in the cathode ray tube, so that the special motion law of electrons in the cathode ray tube can be further explored from both theoretical and experimental aspects.At the same time, it is expected that the theory in this paper can provide theoretical guidance for the manufacture and debugging of electron microscopes and the design of large-scale integrated circuits, and thus influence other related fields...This will involve a vast area of science and technology!This paper is devoted to the in-depth analysis of the objective truth of the wave-particle duality presented by microscopic particles.
As for DE Broglie's hypothesis of matter waves, many experimental physicists have experimentally verified it by using cathode ray tube and proved that matter waves do exist, so there is a mysterious hypothesis of wave-particle duality.In this paper, according to the electric field force of electrons in the cathode ray tube and the continuity equation of electrons, Under assumptions such as inelastic approximation, it is proved that the wave-particle duality is actually the macroscopic motion of real particles in the form of waves.In this paper, it is proved theoretically that the component of electron velocity in the tube satisfies the wave equation, and the wave velocity varies with the change of electric potential in the tube.From the discussion in this paper, it can be seen that there are still some problems to be studied about the motion of electrons in the cathode ray tube, so that the special motion law of electrons in the cathode ray tube can be further explored from both theoretical and experimental aspects.At the same time, it is expected that the theory in this paper can provide theoretical guidance for the manufacture and debugging of electron microscopes and the design of large-scale integrated circuits, and thus influence other related fields...This will involve a vast area of science and technology!This paper is devoted to the in-depth analysis of the objective truth of the wave-particle duality presented by microscopic particles.
This article aims to reveal the truth behind the formation of de Broglie waves and clarify the mysterious assumptions such as wave-particle duality and probability waves, which people are familiar with but do not understand the reasons behind.On the towering tree of physics, the branch concerning the interpretation of de Broglie waves has grown crooked!This article intends to sprout new buds at this node to promote the progress and prosperity of physics!Based on the electric field force that electrons experience in a cathode ray tube and the continuity equation of electrons, under assumptions such as the non-elastic approximation, this article proves that wave-particle duality is actually the macroscopic movement of microscopic particles in the form of waves.Theoretically, it is demonstrated that the transverse component of the electron's velocity in the tube satisfies a nonlinear inhomogeneous wave equation.The equations of this type should describe a complex system: under certain parameters, the system may be extremely sensitive to initial conditions, showing chaotic characteristics, and its output is extremely complex and difficult to predict over the long term.This is the uncertainty in quantum mechanics!The conclusion of this article indicates that this is a new form of wave, that is, the form of waves not only includes the propagation of vibrations but also the macroscopic movement of microscopic particles in the form of waves.Therefore, this wave can transport material particles from one end to the other in the form of waves!Moreover, this article discusses a single electron, so even if the electrons are emitted one by one, their wave characteristics can still be observed on the screen!From the discussion in this article, it can be seen that there are still some problems with the movement of electrons in the cathode ray tube that need to be solved in order to further explore the special movement laws of electrons in the cathode ray tube from both theoretical and experimental aspects.At the same time, it is hoped that the theory in this article can provide theoretical guidance for the manufacture and debugging of electron microscopes and the design of large-scale integrated circuits, thereby influencing other related How to cite this paper: Chen, Y.C.
The author has worked with high-resolution transmission electron microscope for many years, which provides the most direct evidence of wave-particle duality. This relates to Crookes and J. J. Thomson's cathode rays tubes to determine that electron beams are of particle nature. This also relates to Röntgen's discovery that when an electron beam in the cathode rays tube strikes the glass wall, it produces X-rays with extremely high penetrating power. This behavior is consistent with Maxwell-Lorentz’s electrodynamics that electromagnetic waves must be produced whenever electricity carriers alter their velocity. The wave-particle duality proposed by de Broglie refers to accelerated electron beam, rather than single electron. De Broglie emphasized that the crystallographic diffraction pattern produced by his electron beam was completely consistent with the crystallographic diffraction pattern of von Laue by X-rays, therefore, he proposed that electrons possess wave-particle duality. This is actually the selected area electron diffraction pattern in transmission microscope. It is X-rays, not the waves of the electrons themselves to produce diffraction pattern. He extended this to the wave-particle duality of all matter and light. Schrödinger directly introduced de Broglie's electron beam behavior into electron wave in atoms. It was just at this stage that illogical reasoning occurred, making the quantum theory increasingly difficult to understand.
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.
To members of the British Institute of Radiology the cathode ray is probably most familiar as the necessary antecedent of X rays. You are interested in them chiefly as a means to an end, but the cathode rays had a very real intrinsic interest in the nineties of last century. It was the study of the beam of light in a low-pressure discharge tube which led to the recognition of the existence of a universal constituent of matter—the electron—and I hope to show that the importance of cathode rays for the study of fundamental problems in physics is not yet exhausted. The cathode rays still form in many respects the most convenient way of studying the properties if electrons. Of recent years our views on the nature of these electrons have undergone a striking change, as a result of the brilliant inspiration of Prince Louis de Broglie, who has been rewarded with a Nobel Prize. He founded the theory which is now dominant in physics under the name of wave mechanics, and which is a general theory of the behaviour of any form of particle. According to this view all particles are associated with some form of wave, the properties of which determine much of the behaviour of the particle. This theory was originally devised by de Broglie from considerations based upon relativity.
This chapter describes the dual nature of electron/de Broglie waves. de Broglie suggested that like light, an electron also behaves as both a particle and a wave. Based on this hypothesis, a relationship between wavelength of electrons (a particle) and momentum was developed. It opines that ‘wavelength of the particle is inversely proportional to momentum’. This is called the de Broglie relation. On the basis of the above facts, we have developed a relationship between wavelength and voltage applied and this relation may be stated as ‘the wavelength of a particle is inversely proportional to the square root of the voltage applied to the system’. This chapter also uses the Davisson and Germer experiment to show the wave nature of the particle, i.e., diffraction of electrons by crystal lattice. The experimental results were the same as found in the case of the diffraction of X-ray by crystals. This chapter also provides an idea on quantisation of angular momentum. It also discusses Heisenberg’s uncertainty principle, phase velocity, group velocity, and uncertainty relation between energy and time. The chapter comprises the experimental evidence of Heisenberg’s uncertainty principle, such as by diffraction of electrons through a slit and gamma ray microscope thought experiment, which is shows the physical significance of the uncertainty principle. Sufficient references, solved problems, and questions on concepts have been provided at the end of chapter.
In 1924, de Broglie postulated that particles can behave like waves, thus complementing the observation by Einstein in 1905 that light can behave like particles. This wave–particle duality aspect for both particles and waves had a deep impact on the subsequent development of quantum mechanics. Some highly counterintuitive results, like the Heisenberg uncertainty relation and the Bose–Einstein condensation, that were motivated by wave–particle duality are discussed in this chapter. Following de Broglie’s hypothesis, a wave packet description for a particle is described. An analysis of the Heisenberg microscope is presented, thus motivating the Heisenberg uncertainty relation. The Davisson–Germer experiment that showed that electrons can behave like waves and the Compton effect that provided early conclusive evidence that light can behave like particles are also discussed.