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.
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.
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.
Abstract 1. M. L. de Broglie has introduced a theory of mechanics according to which a moving particle behaves as a group of waves whose velocity and wave-length are governed by the speed and mass of the particle. In fact if m0 is the mass for slow speed and v the speed of a freely moving particle, the wave-length is given by λ = h√1-v2/c2 / m0v, and the wave velocity V by V = c2/v, the group velocity being v, the velocity of the particle. Here c is the velocity of light and it will be seen that the wave velocity is greater than c. There is nothing impossible in this because the waves are regarded as purely geometrical —“phase waves”—not as carrying energy. Compare, in ordinary optical theory, the case of substances, such as sodium, for which the refractive index is less than unity. The above is for free space; in the presence of a field of force V varies, and the consequent bending of the waves by refraction corresponds, on the new theory, to the deviation of the path of the particle by the field of force, on the old. The consequences of this theory have been worked out by de Broglie, Schrödinger and others and applied to problems in spectroscopy where they have provided the solution of several outstanding difficulties left by the older theory of orbits. In view, however, of the extremely fundamental nature of the theory it is highly desirable that it should rest on more direct evidence, and, in particular, that it should be shown capable of predicting as well as of merely explaining. Dymond has obtained some remarkable results on the scattering of slow electrons in helium which are of the general nature to be expected in this theory, but our knowledge of the structure of helium, together with the mathematical difficulties of the problem have so far prevented any exact comparision of the theory with experiment. Davisson and Kunsman and Davisson and Germer have obtained results on the reflection of slow electrons from the surfaces of crystals, especially nickel, which show good qualitative agreement with the theory but a discrepancy of 30 per cent. in certain magnitudes. It is hoped that the experiments described in this paper will advance the matter a stage further. They are a development of some experiments of which a preliminary account appeared recently in ‘Nature.’
Among the secondary effects produced in an X-ray, or cathode ray tube, there is one which is of special interest to physicists because it seems to throw some light on the question as to the nature of an electron. It appears that when a pencil of cathode rays falls upon the surface of a metal crystal, some of the rays are reflected, or “scattered,” and that the intensity of the scattered rays is greatest in certain directions, so that on a photographic plate placed to receive them, a diffraction pattern is produced as with X rays. The experiment proves that electrons, which were till recently supposed to be merely “particles,” really consist (like X rays), of waves, or at any rate have waves associated with them. It is to these waves associated with electrons, or “electron waves” as they are called, that I propose to devote my remarks this evening. The effect was first observed experimentally in 1927, by Davisson and Germer, who reflected cathode rays from a nickel crystal and, using an electrical method of detection, found maxima of intensity in certain directions. From the positions of the maxima and the known spacing constants of nickel they were able to deduce the wave-length of the electron waves. Later in the same year Professor G. P. Thomson obtained similar effects by transmitting cathode rays through thin metal films and receiving them on a photographic plate.
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.
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.
Where did we get that [equation] from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger. Richard Feynman De Broglie's matter waves The early struggles of physicists towards a quantum theory were mostly concerned with attempts to understand the nature of light. The traditional picture of light as a wave motion had been challenged by Planck and Einstein. They had shown that certain experimental results that were impossible to understand in terms of a wave picture could be easily explained if light was thought of as a stream of particles, now called photons. William Bragg, who, with his son, won the 1915 Nobel Prize for studies of crystal structure using X-rays, summarized this dilemma for physics by exclaiming in despair that he was teaching the corpuscular theory of light on Mondays, Wednesdays and Fridays, and the undulatory theory on Tuesdays, Thursdays and Saturdays! Physicists were still wrestling with these apparently contradictory properties of light when, in 1924, Prince Louis de Broglie (pronounced ‘de Broy’) suggested that all matter, even objects that we usually think of as particles – such as electrons – should also display wavelike behaviour! This revolutionary idea was completely unexpected and, what is more, was included by de Broglie in his Ph. D. thesis. Like most people, physicists are generally reluctant to accept any wild new idea, especially if there is not a shred of evidence to support it.