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Matter Waves Proposed by de Broglie (1923)

S. Brandt

Published Apr 22, 1992• 0 citations
Publisher

Abstract

Abstract We have seen that it took about two decades to fully realize that light or, generally, electromagnetic radiation has both wave and particle properties. The final proof came with the discovery of the Compton effect (Episode 31). Even Compton himself needed years before he saw that the particle picture of radiation was unavoidable in view of the experimental evidence. Still in the year of Compton’s publications, Louis de Broglie [1] on purely theoretical grounds proposed that the particle–wave duality not only holds for radiation but also for material particles, i.e., for particles with a rest mass such as the electron.

DOI
10.1093/oso/9780199544691.003.0033

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Abstract We have seen that it took about two decades to fully realize that light or, generally, electromagnetic radiation has both wave and particle properties. The final proof came with the discovery of the Compton effect (Episode 31). Even Compton himself needed years before he saw that the particle picture of radiation was unavoidable in view of the experimental evidence. Still in the year of Compton’s publications, Louis de Broglie [1] on purely theoretical grounds proposed that the particle–wave duality not only holds for radiation but also for material particles, i.e., for particles with a rest mass such as the electron.
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.
Abstract The particle-wave duality was perhaps the most startling outcome of the conceptual revolution that swept through physics during the first three decades of the twentieth century. That photons—the packets, or quanta, of light— behaved in some respects as particles, in others as waves, had already been noted when the due (later Prince) Louis de Broglie conjectured that the same might be true of other particles, such as electrons. Sitting in an eyrie in the Eiffel Tower as a meteorological observer during the First World War, de Broglie had time to ruminate on these matters and to develop an equation relating the momentum of the particle to its wavelength. This formed the substance of his doctoral dissertation, which he submitted to the University of Paris in 1924 and which earned him the Nobel Prize five years later.
Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles also have a wave nature (and vice versa).[1] This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected.[2] Wave–particle duality is an ongoing conundrum in modern physics. Most physicists accept wave-particle duality as the best explanation for a broad range of observed phenomena; however, it is not without controversy.
A group of electrons that traverses a sufficiently small aperture will exhibit diffraction effects. It is not entirely surprising that the earliest reaffirmation of the dualism inherent in radiation came neither from Britain nor Germany. There the issues had been recognized, discussed, and dismissed over the preceding twenty years. And American research traditions were largely derivative of German and British models; Duane and Millikan had both studied under Planck, and Richardson did research with Thomson in Cambridge. It took an outsider to these traditions to raise the issues in a way that began to convince others. That process began in France. Maurice and Louis de Broglie were, by any standards, unusual physicists. Amateurs in an age of professionals, possessing a confidence born of noble status, working on experiments that had only the meagerest precedent in their homeland, they were not as firmly bound by the predispositions that prevented physicists of other nations from directly assessing the spatially localized lightquantum. Their conversion was real. Maurice had once been convinced that x-rays and γ-rays fit neatly into the electromagnetic spectrum. In his discussion, La nature des rayons de Röntgen in 1915, there was no thought that x-rays might be anything other than periodic waves. As late as May 1920, he spoke freely of x-ray “wavelengths” and discussed the optical fluorescence that results from degradation of x-ray “frequency.” But late in 1920 he reviewed the new evidence accumulated at high x-ray frequencies. There he hinted at unspecified difficulties in the orthodox wave interpretation of x-rays.
The Compton effect is commonly cited as a demonstration of the particle feature of light, while the wave nature of matter has been proposed by de Broglie and demonstrated by Davisson and Germer with the Bragg diffraction of electron beams. In this investigation, we present an entirely different interpretation of the Compton effect based on the postulates of de Broglie and on an interaction between electromagnetic and matter waves. The speeds of interacting electrons in the Compton scattering are quite fast and its mechanism relies heavily on the mass variation. Thus, based on this wave interpretation, the Compton effect can be viewed as a further demonstration of the postulates of de Broglie for high-speed particles. In addition to the scattered wave, a direct radiation depending on the mass variation is predicted, which provides a means to test the wave interpretation.
Abstract The contributions of Otto Stern to the discovery of wave-particle duality of matter particles predicted by de Broglie are reviewed. After a short introduction to the early matter-vs-wave ideas about light, the events are highlighted which lead to de Broglie’s idea that all particles, also massive particles, should exhibit wave behavior with a wavelength inversely proportional to their mass. The first confirming experimental evidence came for electrons from the diffraction experiments of Davisson and Germer and those of Thomson. The first demonstration for atoms, with three orders of magnitude smaller wave lengths, came from Otto Stern’s laboratory shortly afterwards in 1929 in a remarkabletour de forceexperiment. After Stern’s forced departure from Hamburg in 1933 it took more than 40 years to reach a similar level of experimental perfection as achieved then in Stern’s laboratory. Today He atom diffraction is a powerful tool for studying the atomic and electronic structure and dynamics of surfaces. With the advent of nanotechnology nanoscopic transmission gratings have led to many new applications of matter waves in chemistry and physics, which are illustrated with a few examples and described in more detail in the following chapters.