de broglie doctoral thesis

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5 Further steps to quantum mechanics: Louis de Broglie and the world’s most important PhD thesis

• Published: February 2023
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Working on his Ph.D. thesis, Louis de Broglie asked himself this question: If light, thought to be a wave motion because of observed interference and diffraction effects, could behave like a particle, might particles exhibit some wave-like properties? He justified this idea with several arguments which are highly relevant to an understanding of quantum theory. Among these was the fact that the Bohr-Sommerfeld condition can be derived from the association of a wave with particle motion. This was a critically significant step in the development of quantum mechanics. This work was presented in a relatively short Ph.D. dissertation.

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 MacTutor

Louis victor pierre raymond duc de broglie.

When in 1920 I resumed my studies ... what attracted me ... to theoretical physics was ... the mystery in which the structure of matter and of radiation was becoming more and more enveloped as the strange concept of the quantum , introduced by Planck in 1900 in his researches into black-body radiation, daily penetrated further into the whole of physics.

Thirty years ago, physics was divided into two camps: ... the physics of matter, based on the concepts of particles and atoms which were supposed to obey the laws of classical Newtonian mechanics, and the physics of radiation, based on the idea of wave propagation in a hypothetical continuous medium, the luminous and electromagnetic ether. But these two systems of physics could not remain detached from each other: they had to be united by the formulation of a theory of exchanges of energy between matter and radiation. ... In the attempt to bring the two systems of physics together, conclusions were in fact reached which were neither correct nor even admissible when applied to the energy equilibrium between matter and radiation ... Planck ... assumed ... that a light source ... emits its radiation in equal and finite quantities - in quanta. The success of Planck 's ideas has been accompanied by serious consequences. if light is emitted in quanta, must it not, once emitted, possess a corpuscular structure? ... Jeans and Poincaré [ showed ] that if the motion of the material particles in a source of light took place according to the laws of classical mechanics, then the correct law of black-body radiation, Planck 's law, could not be obtained.

As in my conversations with my brother we always arrived at the conclusion that in the case of X-rays one had both waves and corpuscles, thus suddenly - ... it was certain in the course of summer 1923 - I got the idea that one had to extend this duality to material particles, especially to electrons. And I realised that, on the one hand, the Hamilton - Jacobi theory pointed somewhat in that direction, for it can be applied to particles and, in addition, it represents a geometrical optics; on the other hand, in quantum phenomena one obtains quantum numbers, which are rarely found in mechanics but occur very frequently in wave phenomena and in all problems dealing with wave motion.

Thus I arrived at the following general idea which has guided my researches: for matter, just as much as for radiation, in particular light, we must introduce at one and the same time the corpuscle concept and the wave concept. In other words, in both cases we must assume the existence of corpuscles accompanied by waves. But corpuscles and waves cannot be independent, since, according to Bohr, they are complementary to each other; consequently it must be possible to establish a certain parallelism between the motion of a corpuscle and the propagation of the wave which is associated with it.

... having much more the state of mind of a pure theoretician than that of an experimenter or engineer, loving especially the general and philosophical view ... .

... the statistical theories hide a completely determined and ascertainable reality behind variables which elude our experimental techniques.

When quite young you threw yourself into the controversy raging round the most profound problem in physics. You had the boldness to assert, without the support of any known fact, that matter had not only a corpuscular nature, but also a wave nature. Experiment came later and established the correctness of your view. You have covered in fresh glory a name already crowned for centuries with honour.

References ( show )

• J L Heilbron, A R Weill-Brunschvicg, Biography in Dictionary of Scientific Biography ( New York 1970 - 1990) . See THIS LINK .
• Biography in Encyclopaedia Britannica. https://www.britannica.com/biography/Louis-de-Broglie
• B L Cline, The Questioners: Physicists and the Quantum Theory (1965) .
• Louis de Broglie que nous avons connu, Fondation Louis de Broglie ( Paris, 1988) .
• A Abragam, Louis de Broglie : la grandeur et la solitude, La Recherche 245 (1992) , 918 - 923 .
• S Colombo, Louis de Broglie 1892 - 1987 , Revue des questions scientifiques 162 (1991) , 349 - 359 .
• M Eberhardt, La France a perdu un genie, Science et vie 836 (1987) , 10 - 25 , 160 .
• L de Guitton, Le duc Louis de Broglie : témoignage sur l'homme que j'ai connu, Comptes rendus de l'Academie des sciences 9 (1992) , 331 - 334 .
• N H de V Heathcote, Prince Louis-Victor de Broglie, Nobel prize winners in physics, 1901 - 1950 ( New York, 1953) , 287 - 296 .
• L Michel, Louis de Broglie : le savant, La Recherche 245 (1992) , 923 -.

Additional Resources ( show )

Other pages about Louis de Broglie:

• Miller's postage stamps

Other websites about Louis de Broglie:

• Dictionary of Scientific Biography
• Encyclopaedia Britannica
• Nobel prizes site ( A biography of de Broglie and his Nobel prize presentation speech )
• Académie Française; ( in French )
• Mathematical Genealogy Project
• MathSciNet Author profile
• zbMATH entry

Honours ( show )

Honours awarded to Louis de Broglie

• Nobel Prize 1929
• Fellow of the Royal Society 1953
• Paris street names Rue de Broglie (13 th Arrondissement ) ( also named for his brother ) .

Cross-references ( show )

• History Topics: A history of Quantum Mechanics
• History Topics: Light through the ages: Relativity and quantum era
• History Topics: Wave versus matrix mechanics
• Societies: Pontifical Academy of Sciences
• Other: Jeff Miller's postage stamps

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• Published: 18 May 2023

A century of matter waves

• Alison Wright 1  

Nature Reviews Physics volume  5 ,  pages 318–319 ( 2023 ) Cite this article

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• Quantum physics

One hundred years ago, Louis de Broglie posed a question: could matter particles behave like waves? This duality was already known for light; extending it to electrons and indeed all matter had huge implications, especially for the development of quantum mechanics.

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de Broglie, L. Ondes et quanta. Comptes Rendus 177 , 507–510 (1923).

Google Scholar  

de Broglie, L. Quanta de lumière, diffraction et interfèrences. Comptes Rendus 177 , 548–560 (1923).

de Broglie, L. Les quanta, la théorie cinétique des gaz et le principe de Fermat. Comptes Rendus 177 , 630–632 (1923).

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Quantum Physics

Title: 75 years of matter wave: louis de broglie and renaissance of the causally complete knowledge.

Abstract: A physically real wave associated with any moving particle and travelling in a surrounding material medium was introduced by Louis de Broglie in a series of short notes in 1923 and in a more complete form in his thesis defended in Paris on the 25th November 1924. This result, recognised by the Nobel Prize in 1929, gave rise to a major direction of "new physics" known today as "quantum mechanics". However, although such notions as "de Broglie wavelength" and "wave-particle duality" form the basis of the standard quantum theory, it actually only takes for granted (postulates) the formula for the particle wavelength and totally ignores the underlying causal, realistic and physically transparent picture of wave-particle dynamics outlined by Louis de Broglie in his thesis and further considerably developed in his later works, in the form of "double solution" and "hidden thermodynamics" theory. A price to pay for such rough deviation from the original de Broglian realism and consistency involves fundamental physics domination by purely abstract and mechanistically simplified schemes of formal symbols and rules that have led to a deep knowledge impasse justly described as "the end of science". However, a new, independent approach of "quantum field mechanics" ( quant-ph/9902015 , quant-ph/9902016 , physics/0401164 ) created within the "universal science of complexity" ( physics/9806002 ) provides many-sided confirmation and natural completion of de Broglie's "nonlinear wave mechanics", eliminating all its "difficult points" and reconstituting the causally complete, totally consistent and intrinsically unified picture of the real, complex micro-world dynamics directly extendible to all higher levels of unreduced world complexity.

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The Quantum Theory—Origins and Ideas pp 123–137 Cite as

De Broglie’s Particle Wave

• Carl S. Helrich 7  
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This was an issue he said he would develop, but offered no proof of it.

The time associated with a wave is the period. This is a time interval. The frequency is the reciprocal of the period. If an observer moving with the wave measures the wave period to be \(\tau ^{\prime }\) and a stationary observer measures the period of the moving wave to be \(\tau \) , then

where \(\beta =v/c\) with v the speed of the wave. The frequencies are then related by

At this point de Broglie gave no reason for this particular velocity. He provided his reasoning later, using the relativistic geometry developed by Hermann Minkowski.

The expression \(p=mv\) is also relativistically correct provided m is the relativistic mass.

There was a clear difference between the mission of Bell Telephone Laboratories and the PTR in Berlin-Charlottenburg, Germany.

Gehrenbeck presents an experiment by experiment account of this period [121].

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Helrich, C.S. (2021). De Broglie’s Particle Wave. In: The Quantum Theory—Origins and Ideas. History of Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-79268-8_6

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Richard Schlegel; Louis de Broglie’s thesis. Am. J. Phys. 1 September 1977; 45 (9): 871–872. https://doi.org/10.1119/1.11068

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De Broglie Hypothesis

Does All Matter Exhibit Wave-like Properties?

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The De Broglie hypothesis proposes that all matter exhibits wave-like properties and relates the observed wavelength of matter to its momentum. After Albert Einstein's photon theory became accepted, the question became whether this was true only for light or whether material objects also exhibited wave-like behavior. Here is how the De Broglie hypothesis was developed.

De Broglie's Thesis

In his 1923 (or 1924, depending on the source) doctoral dissertation, the French physicist Louis de Broglie made a bold assertion. Considering Einstein's relationship of wavelength lambda to momentum p , de Broglie proposed that this relationship would determine the wavelength of any matter, in the relationship:

lambda = h / p

recall that h is Planck's constant

This wavelength is called the de Broglie wavelength . The reason he chose the momentum equation over the energy equation is that it was unclear, with matter, whether E should be total energy, kinetic energy, or total relativistic energy. For photons, they are all the same, but not so for matter.

Assuming the momentum relationship, however, allowed the derivation of a similar de Broglie relationship for frequency f using the kinetic energy E k :

f = E k / h

Alternate Formulations

De Broglie's relationships are sometimes expressed in terms of Dirac's constant, h-bar = h / (2 pi ), and the angular frequency w and wavenumber k :

p = h-bar * kE k

= h-bar * w

Experimental Confirmation

In 1927, physicists Clinton Davisson and Lester Germer, of Bell Labs, performed an experiment where they fired electrons at a crystalline nickel target. The resulting diffraction pattern matched the predictions of the de Broglie wavelength. De Broglie received the 1929 Nobel Prize for his theory (the first time it was ever awarded for a Ph.D. thesis) and Davisson/Germer jointly won it in 1937 for the experimental discovery of electron diffraction (and thus the proving of de Broglie's hypothesis).

Further experiments have held de Broglie's hypothesis to be true, including the quantum variants of the double slit experiment . Diffraction experiments in 1999 confirmed the de Broglie wavelength for the behavior of molecules as large as buckyballs, which are complex molecules made up of 60 or more carbon atoms.

Significance of the de Broglie Hypothesis

The de Broglie hypothesis showed that wave-particle duality was not merely an aberrant behavior of light, but rather was a fundamental principle exhibited by both radiation and matter. As such, it becomes possible to use wave equations to describe material behavior, so long as one properly applies the de Broglie wavelength. This would prove crucial to the development of quantum mechanics. It is now an integral part of the theory of atomic structure and particle physics.

Macroscopic Objects and Wavelength

Though de Broglie's hypothesis predicts wavelengths for ​matter of any size, there are realistic limits on when it's useful. A baseball thrown at a pitcher has a de Broglie wavelength that is smaller than the diameter of a proton by about 20 orders of magnitude. The wave aspects of a macroscopic object are so tiny as to be unobservable in any useful sense, although interesting to muse about.

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One day in 1924, a young French noble managed to turned quantum physics on its head, just as it was finding its feet. Even the most conservative physicists were beginning to accept the duality revolution: light is not only a wave, but also behaves like a beam of particles (photons), as Einstein had established with his explanation of the photoelectric effect , which earned him the Nobel Prize in 1921.

Then Louis de Broglie (15 August 1892 – 19 March 1987)—a novice scientist whose first degree was in history—thought otherwise: what if particles also behaved like waves? A century ago there were still questions as attractive as this, to which one might dedicate a doctoral thesis. And that is exactly what de Broglie did. After studying in depth for several years the bases of quantum physics established by Max Planck and Albert Einstein, he presented his thesis in 1924 with an important theoretical discovery: electrons behave as waves and, not only that, all particles and objects are associated with matter waves.

From Einstein’s support to experimental demonstration

This is the well-known de Broglie Hypothesis. Putting together Planck’s equations (quantization of energy: E = hν) and Einstein’s (special relativity: E = mc 2 ), de Broglie calculated what the length of these matter waves associated with each particle would be, depending on its velocity and mass. Thus, according to de Broglie, our whole world is quantum, not just light—a conclusion so bold that it was immediately rejected by many physicists, and ignored by others.

Although in 1924 his scientific career was still short, when he presented his doctoral thesis the French physicist had already done other research, which had led him to clash with some of the most influential physicists of the moment. Not so with Einstein, who enthusiastically supported de Broglie’s conclusions, but even Einstein’s support was not enough to prove him right: his hypothesis had to be experimentally demonstrated.

If the electron were a particle that behaved like a wave, then it would have to show typical properties of waves, such as diffraction and interference. And then some very strange things would happen: for example, one electron would be able to traverse two different holes at the same time. This was demonstrated by the electron diffraction experiment of Davisson and Germer (1927), thus confirming the hypothesis of de Broglie, who was awarded the Nobel Prize for Physics in 1929, just five years after he had presented that bold doctoral thesis.

First step to the electron microscope

Few doctoral theses in the history of science have been so dazzling that they have reached the Nobel with the same work that gave the author the title of doctor. Another great example is that of Marie Curie . Incredibly, Louis de Broglie, with his first great scientific research, succeeded in laying one of the pillars of quantum physics: the wave–particle duality, which states that waves can behave like particles and vice versa. From his idea of matter waves was born wave mechanics, the new formulation of quantum physics that Schrödinger developed to apply to atoms and molecules. And admitting the wave properties of electrons was the basis for inventing the electron microscope (released in 1932), which allows us to see things much smaller than typical optical microscopes permit, because the wavelength of the electron is much shorter than that of photons of visible light.

For all these reasons we remember Louis de Broglie as the ‘prince of quantum’, although in the macroscopic world this scientist aristocrat only became a duke when his brother inherited the duchy de Broglie in 1960. By then, he had already received a multitude of recognitions for his scientific achievements, in addition to the Nobel Prize: he occupied seat 1 of the French Academy (1944), received two prestigious medals—Henri Poincaré (1929) and Max Planck (1938)—and was also the first recipient of the Kalinga Prize (1942), awarded by UNESCO to highlight outstanding contributions to the dissemination of science.

In addition, he was the first world-renowned scientist who called for countries to join forces to meet the great challenges of science in multinational laboratories. CERN (the European Organization for Nuclear Research) was born of this request, and his long life (he passed away at age 94) allowed him to see the exceptional achievements of this particle physics laboratory inspired by his scientific vision.

Francisco Doménech for Ventana al Conocimiento @fucolin

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