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Crystal clear

Walter B. Gratzer

Published Sep 26, 2002• 0 citations
Publisher

Abstract

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.

DOI
10.1093/oso/9780192804037.003.0114

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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.
Louis de Broglie received the Nobel Prize for his Ph.D. It is an extreme statement but not as extreme as one might think. In his 1924 doctoral dissertation, he asserted that all matter had both wave and particle properties. His thesis stemmed from Einstein's recognition that light had particle properties. Until then it was assumed, and every experiment had shown, that light was strictly a wave. With the photoelectric effect explained by Einstein, light became an example of “wave-particle duality.” Before de Broglie, it was the only example. De Broglie proposed that all matter had both wave and particle properties. De Broglie found the relationship between the two: the particle momentum was inversely proportional to the wavelength. Experimental evidence subsequently confirmed his theory, hence the Prize.
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.
Louis-Victor de Broglie secured his place in the history of quantum physics by proposing the existence of matter waves. Following the concept accepted early in the twentieth century that light waves could display properties characteristic of particles (photons), de Broglie suggested the complementary principle that particles could display properties characteristic of waves. Within a few years, this far-reaching proposal was experimentally verified. The well-known formula for the wavelength λ of the wave associated with a particle of momentum p, namely λ=h/p, does not appear in de Broglie’s original paper, which was published in this journal in 1924. What is derived from the starting assumption that the frequency of the wave is the rest energy of the particle divided by Planck’s constant h, is the wave's velocity, which turns out to be c2/v, where v is the particle’s velocity. This velocity, being superluminal, means that the wave cannot transport energy. De Broglie called it a phase wave and postulated a group of such waves having virtually, but not exactly, the same velocity and wavelength. The group velocity of such a large number of almost identical phase waves is then shown, very satisfactorily, to be equal to the velocity of the particle. The proposal by de Broglie inspired Schrödinger to develop the mathematical foundations of wave mechanics. Whereas in conventional quantum theory, phase waves are considered fictional, de Broglie considered them to have a certain physical reality, renaming them pilot or guiding waves – a concept developed later by Bohm in 1952.
In 1924 a young PhD student submitted a thesis containing the germ of an idea that would revolutionize our understanding of the material world.3 e student was Louis De Broglie4 (pronounced De Broy), and for a while he had been meditating on the wave/particle nature of light. In a moment of insight he suddenly realized that the odd behavior of light might extend to other aspects of nature as well. Perhaps particles, such as electrons, could have a wavelike nature to balance the particlelike nature of light, which had been thought of as a wave. Echoing the Planck-Einstein formulas for photons, De Broglie proposed that electrons should have a ‘pilot wave’ with frequency ( f ) and wavelength (λ) given by h mv f E h His thesis also contains an explanation for Bohr’s quantized orbits in hydrogen. If an orbiting electron had a ‘corresponding’ wave, it would have to close on itself around the circular arc of the orbit. is forces the circumference of a satisfactory orbit to be a whole number multiple of the wavelength (see Figure 18.1).
Toward the end of the nineteenth century, it became clear that some experiments cannot be explained on the basis of known physics, now referred to as classical physics. In 1900, Max Planck was able to correctly describe the distribution of blackbody radiation energy as a function of wavelength λ or frequency ν = c/λ. He had to accept the existence of energy packets (quanta) with energy E = hν. A few years later, Albert Einstein found that this unexpected relation between energy and frequency is also necessary in order to understand photoemission from metallic surfaces. A decade later, Niels Bohr arrived at the correct equation for the electronic spectrum of the hydrogen atom by applying “quantum conditions” on the motion of the electron around the nucleus and the Planck’s relation E = hν on the energy difference between the energy levels (1916). A decade later, Heisenberg, Born, and Jordan introduced “quantum mechanics” and de Broglie and Schrödinger (1925-1926) introduced “wave mechanics.”
When in the spring of 1926 Erwin Schrödinger set out the form of the equation for wave propagation and drew important conclusions from it, in some very elegant work which appeared to develop the ideas which I had introduced in 1923–24 (de Broglie 1924), he really profoundly modified the ideas which had guided me two years earlier in my original research. For his idea was that although the ψ wave which he was introducing was still a true physical wave propagated in space and time, it would not have any single area of high field concentration which could be a particle; whereas in my original concept I assumed that the coexistence of waves and particles, perceived by Einstein in 1905 in respect of light in his theory of light quanta, should be extended to all types of particle in the form of the coexistence of a physical wave with a particle incorporated in it.