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Louis de Broglie

From Wikipedia, the free encyclopedia
French theoretical physicist (1892–1987)
"de Broglie" redirects here. For other members of the family, seeHouse of Broglie.

Louis de Broglie
De Broglie in 1929
Born
Louis Victor Pierre Raymond

(1892-08-15)15 August 1892
Died19 March 1987(1987-03-19) (aged 94)
Alma materUniversity of Paris (PhD)
Known for
FatherVictor de Broglie
RelativesMaurice de Broglie (brother)
FamilyBroglie
Awards
Scientific career
FieldsQuantum physics
Institutions
ThesisRecherches sur la théorie des quanta (1924)
Doctoral students

Louis Victor Pierre Raymond, 7th Duc de Broglie (French:[dəbʁɔj];[2] 15 August 1892 – 19 March 1987)[3] was a Frenchtheoretical physicist andaristocrat known for his contributions toquantum theory. In his 1924 Ph.D. thesis, he postulated thewave nature ofelectrons and suggested thatall matter has wave properties. This concept is known as thede Broglie hypothesis, an example ofwave–particle duality, and forms a central part of the theory ofquantum mechanics. In 1929, de Broglie won theNobel Prize in Physics after the wave-like behaviour of matter wasexperimentally confirmed in 1927.[4][5]

The wave-like behaviour of particles theorized by de Broglie was used byErwin Schrödinger in his formulation ofwave mechanics.[6]: 270 De Broglie presented an alternative interpretation of these mechanics called thepilot-wave concept at the 1927Solvay Conferences, but then abandoned it. In 1952,David Bohm developed a new form of the concept which became known as thede Broglie–Bohm theory. De Broglie revisited the idea in 1956, creating another version that incorporated ideas from Bohm andJean-Pierre Vigier.[7]

Louis de Broglie was the sixteenth member elected to occupyseat 1 of theAcadémie française in 1944, and served as Perpetual Secretary of theFrench Academy of Sciences.[8][9] De Broglie became the first high-level scientist to call for establishment of a multi-national laboratory, a proposal that led to the establishment of the European Organization for Nuclear Research (CERN).[10] Among his publications wereThe Revolution in Physics andMatter and Light. He was honorary president of the French Association of Science Writers and received the inauguralKalinga Prize fromUNESCO for his efforts to popularize science.[11][12]

Biography

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Family and education

[edit]
François-Marie, 1st duc de Broglie (1671–1745), ancestor of Louis de Broglie andMarshal of France underLouis XV

Louis Victor Pierre Raymond was born on 15 August 1892 inDieppe, France, into the aristocraticHouse of Broglie, whose representatives for several centuries occupied important military and political posts in France. His father,Louis-Alphonse-Victor, 5th duc de Broglie, was married to Pauline d'Armaille, the granddaughter of theNapoleonic GeneralPhilippe Paul, comte de Ségur, and his wife, the biographerMarie Célestine Amélie d'Armaillé. They had five children; in addition to Louis, these were: Albertina (1872–1946), subsequently the Marquise de Luppé;Maurice (1875–1960), subsequently a famous experimental physicist; Philip (1881–1890), who died two years before the birth of Louis, and Pauline, Comtesse de Pange (1888–1972), subsequently a famous writer.[13] Per theNew York Times, "a great-grandfather fought onGeorge Washington's side in theAmerican Revolutionary War as the chief lieutenant of theMarquis de Lafayette."[5]

As the youngest child in the family, Louis grew up in relative loneliness, read a lot, and was fond of history, especially political. From early childhood, he had a good memory and could accurately read an excerpt from a theatrical production or give a complete list of ministers of theThird Republic of France. For this, he was predicted to become a great statesman in the future.[14]

De Broglie had intended a career inhumanities, and received his first degree (licence ès lettres) in history. Afterwards he turned his attention toward mathematics and physics and received a degree (licence ès sciences) in physics. With the outbreak of theFirst World War in 1914, he offered his services to the army in the development of radio communications.

Military service

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After graduation, de Broglie joined the engineering forces to undergo compulsory service. It began atFort Mont Valérien, but soon, on the initiative of his brother, he was seconded to the Wireless Communications Service and worked on theEiffel Tower, where the radio transmitter was located.[11] Louis de Broglie remained in military service throughout the First World War, dealing with purely technical issues. In particular, together withLéon Brillouin and brother Maurice, he participated in establishing wireless communications with submarines. Louis de Broglie was demobilized in August 1919 with the rank ofadjudant. Later, the scientist regretted that he had to spend about six years away from the fundamental problems of science that interested him.[14][15]

Scientific and pedagogical career

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His 1924 thesisRecherches sur la théorie des quanta[16] (Research on the Theory of the Quanta) introduced his theory ofelectron waves. This included thewave–particle duality theory of matter, based on the work ofMax Planck andAlbert Einstein on light. This research culminated in thede Broglie hypothesis stating thatany moving particle or object had an associated wave. De Broglie thus created a new field in physics, themécanique ondulatoire, or wave mechanics, uniting the physics of energy (wave) and matter (particle). He won theNobel Prize in Physics in 1929 "for his discovery of the wave nature of electrons".[17]

In his later career, de Broglie worked to develop acausal explanation of wave mechanics, in opposition to the whollyprobabilistic models which dominatequantum mechanical theory; it was refined byDavid Bohm in the 1950s. The theory has since been known as theDe Broglie–Bohm theory.

In addition to strictly scientific work, de Broglie thought and wrote about thephilosophy of science, including the value of modern scientific discoveries. In 1930 he founded the book series Actualités scientifiques et industrielles published byÉditions Hermann.[18]

De Broglie became a member of theAcadémie des sciences in 1933, and was the academy's perpetual secretary from 1942. He was asked to joinLe Conseil de l'Union Catholique des Scientifiques Francais, but declined because he was non-religious.[19][20]In 1941, he was made a member of the National Council ofVichy France.[21] On 12 October 1944, he was elected to theAcadémie Française, replacing mathematicianÉmile Picard. Because of the deaths and imprisonments of Académie members during the occupation and other effects of the war, the Académie was unable to meet the quorum of twenty members for his election; due to the exceptional circumstances, however, his unanimous election by the seventeen members present was accepted. In an event unique in the history of the Académie, he was received as a member by his own brother Maurice, who had been elected in 1934.UNESCO awarded him the firstKalinga Prize in 1952 for his work in popularizing scientific knowledge, and he was elected a Foreign Member of theRoyal Society on 23 April 1953.[11]

Louis became the 7thduc de Broglie in 1960 upon the death without heir of his elder brother,Maurice, 6th duc de Broglie, also a physicist.

In 1961, de Broglie received the title of Knight of the Grand Cross in theLégion d'honneur. De Broglie was awarded a post as counselor to the French High Commission of Atomic Energy in 1945 for his efforts to bring industry and science closer together. He established a center for applied mechanics at theHenri Poincaré Institute, where research into optics, cybernetics, and atomic energy were carried out. He inspired the formation of theInternational Academy of Quantum Molecular Science and was an early member.[22]

De Broglie never married. When he died on 19 March 1987 inLouveciennes at the age of 94,[3] he was succeeded asduke by a distant cousin,Victor-François, 8th duc de Broglie. His funeral was held 23 March 1987 at the Church of Saint-Pierre-de-Neuilly.[23]

Research

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Physics of X-ray and photoelectric effect

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The first works of Louis de Broglie (early 1920s) were performed in the laboratory of hisolder brother Maurice and dealt with the features of thephotoelectric effect and the properties ofx-rays. These publications examined the absorption of X-rays and described this phenomenon using theBohr theory, applied quantum principles to the interpretation ofphotoelectron spectra, and gave a systematic classification of X-ray spectra.[14] The studies of X-ray spectra were important for elucidating the structure of the internal electron shells of atoms (optical spectra are determined by the outer shells). Thus, the results of experiments conducted together with Alexandre Dauvillier, revealed the shortcomings of the existing schemes for the distribution of electrons in atoms; these difficulties were eliminated byEdmund Stoner.[24] Another result was the elucidation of the insufficiency of the Sommerfeld formula for determining the position of lines in X-ray spectra; this discrepancy was eliminated after the discovery of the electron spin. In 1925 and 1926, Leningrad physicistOrest Khvolson nominated the de Broglie brothers for the Nobel Prize for their work in the field of X-rays.[13]

Matter and wave–particle duality

[edit]
Main article:De Broglie hypothesis

Studying the nature of X-ray radiation and discussing its properties with his brother Maurice, who considered these rays to be some kind of combination of waves and particles, contributed to Louis de Broglie's awareness of the need to build a theory linking particle and wave representations. In addition, he was familiar with the works (1919–1922) ofMarcel Brillouin, which proposed a hydrodynamic model of an atom and attempted to relate it to the results of Bohr's theory. The starting point in the work of Louis de Broglie was the idea of Einstein about thequanta of light. In his first article on this subject, published in 1922, the French scientist considered blackbody radiation as a gas of light quanta and, using classical statistical mechanics, derived theWien radiation law in the framework of such a representation. In his next publication, he tried to reconcile the concept of light quanta with the phenomena of interference and diffraction and came to the conclusion that it was necessary to associate a certain periodicity with quanta. In this case, light quanta were interpreted by him as relativistic particles of very small mass.[25]

It remained to extend the wave considerations to any massive particles, and in the summer of 1923 a decisive breakthrough occurred. De Broglie outlined his ideas in a short note "Waves and quanta" (French:Ondes et quanta, presented at a meeting of the Paris Academy of Sciences on September 10, 1923),[26] which marked the beginning of the creation of wave mechanics. In this paper and his subsequent PhD thesis,[16] the scientist suggested that a moving particle with energyE and velocityv is characterized by some internal periodic process with a frequencyE/h{\displaystyle E/h} (later known asCompton frequency), whereh{\displaystyle h} is thePlanck constant. To reconcile these considerations, based on the quantum principle, with the ideas of special relativity, de Broglie associated wave he called a "phase wave" with a moving body, which propagates with thephase velocityc2/v{\displaystyle c^{2}/v}. Such a wave, which later received the namematter wave, orde Broglie wave, in the process of body movement remains in phase with the internal periodic process. Having then examined the motion of an electron in a closed orbit, the scientist showed that the requirement for phase matching directly leads to the quantumBohr-Sommerfeld condition, that is, to quantize the angular momentum. In the next two notes (reported at the meetings on September 24 and October 8, respectively), de Broglie came to the conclusion that the particle velocity is equal to thegroup velocity of phase waves, and the particle moves along the normal to surfaces of equal phase. In the general case, the trajectory of a particle can be determined usingFermat's principle (for waves) or theprinciple of least action (for particles), which indicates a connection between geometric optics and classical mechanics.[27] Thede Broglie wavelengthλ is thePlanck constanth divided bymomentump:λ=hp.{\displaystyle \lambda ={\frac {h}{p}}.}

This theory set the basis of wave mechanics. It was supported by Albert Einstein,[28] confirmed by theelectron diffraction experiments ofGeorge Paget Thomson in the United Kingdom andClinton Davisson andLester Germer in the United States, and generalized by the work of Erwin Schrödinger.[29]

Originally, de Broglie thought that real wave (i.e., having a direct physical interpretation) was associated with particles. However, when the wave aspect of matter was formalized by awavefunction defined by theSchrödinger equation, it came out as a pure mathematical entity having aprobabilistic interpretation, without the support of physical elements. This wavefunction gives wave behavior to matter but it is only observed through individual quantum samples. However, in 1956 de Broglie again attempted a theory of a direct and physical interpretation of matter-waves, following the work ofDavid Bohm and suggestions ofJean-Pierre Vigier.[7]

Conjecture of an internal clock of the electron

[edit]
de Broglie presented at the Solvay conference 1927 (third from right in middle row).

In his 1924 thesis, de Broglie conjectured that the electron has an internal clock that constitutes part of the mechanism by which apilot wave guides a particle.[30] Subsequently,David Hestenes has proposed a link to thezitterbewegung that was suggested by Schrödinger.[31]

While attempts at verifying the internal clock hypothesis and measuring clock frequency are so far not conclusive,[32] recent experimental data is at least compatible with de Broglie's conjecture.[33]

Non-nullity and variability of mass

[edit]

According to de Broglie, theneutrino and thephoton have rest masses that are non-zero, though very low. That a photon is not quite massless is imposed by the coherence of his theory. Incidentally, this rejection of the hypothesis of a massless photon enabled him to doubt the hypothesis of the expansion of the universe.

In addition, he believed that the true mass of particles is not constant, but variable, and that each particle can be represented as athermodynamic machine equivalent to a cyclic integral of action.

Generalization of the principle of least action

[edit]
See also:Hamilton's optico-mechanical analogy

In the second part of his 1924 thesis, de Broglie used the equivalence of the mechanical principle of least action withFermat's optical principle: "Fermat's principle applied to phase waves is identical toMaupertuis' principle applied to the moving body; the possible dynamic trajectories of the moving body are identical to the possible rays of the wave." This latter equivalence had been pointed out byWilliam Rowan Hamilton a century earlier, and published by him around 1830, for the case of light.

Duality of the laws of nature

[edit]

Far from claiming to make "the contradiction disappear" whichMax Born thought could be achieved with a statistical approach, de Broglie extended wave–particle duality to all particles (and to crystals which revealed the effects of diffraction) and extended the principle of duality to thelaws of nature.

His last work made a single system of laws from the two large systems of thermodynamics and of mechanics:[citation needed]

WhenBoltzmann and his continuators developed their statistical interpretation of Thermodynamics, one could have considered Thermodynamics to be a complicated branch of Dynamics. But, with my actual ideas, it's Dynamics that appear to be a simplified branch of Thermodynamics. I think that, of all the ideas that I've introduced in quantum theory in these past years, it's that idea that is, by far, the most important and the most profound.

That idea seems to match the continuous–discontinuous duality, since its dynamics could be the limit of its thermodynamics when transitions to continuous limits are postulated. It is also close to that ofGottfried Wilhelm Leibniz, who posited the necessity of "architectonic principles" to complete the system of mechanical laws.[citation needed]

However, according to him, there is less duality, in the sense of opposition, than synthesis (one is the limit of the other)[citation needed] and the effort of synthesis is constant according to him, like in his first formula, in which the first member pertains to mechanics and the second to optics:

mc2=hν{\displaystyle mc^{2}=h\nu }

Neutrino theory of light

[edit]
Main article:Neutrino theory of light

This theory, which dates from 1934, introduces the idea that the photon is equivalent to the fusion of twoDirac neutrinos.[34] In 1938, the concept was challenged as not rotationally invariant and work on the concept was largely discontinued.[35]

Hidden thermodynamics

[edit]

De Broglie's final idea was the hidden thermodynamics of isolated particles. It is an attempt to bring together the three furthest principles of physics: the principles of Fermat, Maupertuis, andCarnot.

In this work,action becomes a sort of opposite toentropy, through an equation that relates the only two universal dimensions of the form:

actionh=entropyk{\displaystyle {{\text{action}} \over h}=-{{\text{entropy}} \over k}}

As a consequence of its great impact, this theory brings back theuncertainty principle to distances around extrema of action, distances corresponding toreductions in entropy.

Awards

[edit]

Jean-Claude Lehmann, director of the physics department at France's National Center for Scientific Research, said, "The death of Louis de Broglie marks the disappearance of one of the most brilliant pioneers in contemporary physics".[5]

Publications

[edit]
Ondes et mouvements, 1926
  • Recherches sur la théorie des quanta (Researches on the quantum theory), Thesis, Paris, 1924, Ann. de Physique (10)3, 22 (1925).
  • Introduction à la physique des rayons X et gamma (Introduction to physics of X-rays and Gamma-rays), withMaurice de Broglie, Gauthier-Villars, 1928.
  • Ondes et mouvements (in French). Paris: Gauthier-Villars. 1926.
  • Rapport au 5ème Conseil de Physique Solvay (Report for the 5th Solvay Physics Congress), Brussels, 1927.
  • Mecanique ondulatoire (in French). Paris: Gauthier-Villars. 1928.
  • Recueil d'exposés sur les ondes et corpuscules (in French). Paris: Librairie scientifique Hermann et C.ie. 1930.
  • Matière et lumière (Matter and Light), Paris: Albin Michel, 1937.
  • La Physique nouvelle et les quanta (New Physics and Quanta), Flammarion, 1937.
  • Continu et discontinu en physique moderne (Continuous and discontinuous in Modern Physics), Paris: Albin Michel, 1941.
  • Ondes, corpuscules, mécanique ondulatoire (Waves, Corpuscles, Wave Mechanics), Paris: Albin Michel, 1945.
  • Physique et microphysique (Physics and Microphysics), Albin Michel, 1947.
  • Vie et œuvre de Paul Langevin (The life and works ofPaul Langevin), French Academy of Sciences, 1947.
  • Optique électronique et corpusculaire (Electronic and Corpuscular Optics), Herman, 1950.
  • Savants et découvertes (Scientists and discoveries), Paris, Albin Michel, 1951.
  • Une tentative d'interprétation causale et non linéaire de la mécanique ondulatoire: la théorie de la double solution. Paris: Gauthier-Villars, 1956.
    • English translation:Non-linear Wave Mechanics: A Causal Interpretation. Amsterdam: Elsevier, 1960.
  • Nouvelles perspectives en microphysique (New prospects in Microphysics), Albin Michel, 1956.
  • Sur les sentiers de la science (On the Paths of Science), Paris: Albin Michel, 1960.
  • Introduction à la nouvelle théorie des particules de M.Jean-Pierre Vigier et de ses collaborateurs, Paris: Gauthier-Villars, 1961. Paris: Albin Michel, 1960.
    • English translation:Introduction to the Vigier Theory of elementary particles, Amsterdam: Elsevier, 1963.
  • Étude critique des bases de l'interprétation actuelle de la mécanique ondulatoire, Paris: Gauthier-Villars, 1963.
    • English translation:The Current Interpretation of Wave Mechanics: A Critical Study, Amsterdam, Elsevier, 1964.
  • Certitudes et incertitudes de la science (Certitudes and Incertitudes of Science). Paris: Albin Michel, 1966.
  • with Louis Armand, Pierre Henri Simon and others.Albert Einstein. Paris: Hachette, 1966.
    • English translation:Einstein. Peebles Press, 1979.[40]
  • Recherches d'un demi-siècle (Research of a half-century), Albin Michel, 1976.
  • Les incertitudes d'Heisenberg et l'interprétation probabiliste de la mécanique ondulatoire (Heisenberg uncertainty and wave mechanics probabilistic interpretation), Gauthier-Villars, 1982.

References

[edit]
  1. ^abcdefg"Louis de Broglie - The Mathematics Genealogy Project".genealogy.math.ndsu.nodak.edu. Retrieved2 June 2025.
  2. ^The interviewer pronounces de Broglie's name before asking questions of the scientist.Nomen Nominandum (28 January 2016).Interview with Louis de Broglie, 1967 (French with English Subtitles). Retrieved18 September 2025 – via YouTube.
  3. ^abLeroy, Francis (2003).A Century of Nobel Prize Recipients: Chemistry, Physics, and Medicine (illustrated ed.). CRC Press. p. 141.ISBN 0-8247-0876-8.Extract of page 141
  4. ^"The Nobel Prize in Physics 1929".The Nobel Foundation.
  5. ^abcEnnis, Thomas W. (20 March 1987)."LOUIS DE BROGLIE, FRENCH PHYSICIST, WON '29 NOBEL PRIZE FOR WAVE THEORY".The New York Times.
  6. ^Whittaker, Edmund T. (1989).A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ.ISBN 978-0-486-26126-3.
  7. ^abBridgman, P. W.; de Broglie, Louis; Knodel, Arthur J.; Miller, Jack C. (1960)."Review of Non-Linear Wave Mechanics: A Causal Interpretation, de BroglieLouis, KnodelArthur J., MillerJack C."Scientific American.203 (4):201–206.doi:10.1038/scientificamerican1060-201.ISSN 0036-8733.JSTOR 24940668.
  8. ^O'Connor, John J.;Robertson, Edmund F.,"Louis de Broglie",MacTutor History of Mathematics Archive,University of St Andrews
  9. ^"History of International Academy of Quantum Molecular Science". IAQMS. Retrieved8 March 2010.
  10. ^"Louis de Broglie". Soylent Communications. Retrieved12 June 2015.
  11. ^abc"Louis de Broglie - Biographical".The Nobel Foundation.
  12. ^"NOTES ON SCIENCE: First Award of Kalinga Prize -- Best Light for Eyes".The New York Times. 15 June 1952.
  13. ^abM. J. Nye. (1997). "Aristocratic Culture and the Pursuit of Science: The De Broglies in Modern France".Isis.88 (3) (Isis ed.):397–421.doi:10.1086/383768.JSTOR 236150.S2CID 143439041.
  14. ^abcA. Abragam. (1988). "Louis Victor Pierre Raymond de Broglie".Biographical Memoirs of Fellows of the Royal Society.34:22–41.doi:10.1098/rsbm.1988.0002.
  15. ^J. Lacki. (2008).New Dictionary of Scientific Biography. Vol. 1. Detroit: Charles Scribner's Sons. pp. 409–415.
  16. ^abde Broglie, Louis Victor."On the Theory of Quanta"(PDF).Foundation of Louis de Broglie (English translation by A.F. Kracklauer, 2004. ed.). Retrieved2 January 2020.
  17. ^"The Nobel Prize in Physics 1929".The Nobel Foundation.
  18. ^Recherche (PPN) 01331081X: Actualités scientifiques et industrielles, sudoc.fr. Retrieved 11 December 2021.
  19. ^Evans, James; Thorndike, Alan S. (2007).Quantum Mechanics at the Crossroads: New Perspectives From History, Philosophy And Physics. Springer. p. 71.ISBN 9783540326632.Asked to join Le Conseil de l'Union Catholique des Scientifiques Français, Louis declined because, he said, he had ceased the religious practices of his youth.
  20. ^Kimball, John (2015). Physics Curiosities, Oddities, and Novelties. CRC Press. p. 323.ISBN 978-1-4665-7636-0.
  21. ^ Les professeurs de la Faculté des sciences de Paris[1]
  22. ^Piotr Piecuch; Jean Maruani; Gerardo Delgado-Barrio; Stephen Wilson (30 September 2009).Advances in the Theory of Atomic and Molecular Systems: Conceptual and Computational Advances in Quantum Chemistry. Springer Science & Business Media. p. 4.ISBN 978-90-481-2596-8.
  23. ^Louis Néel; Fondation Louis de Broglie; Conservatoire national des arts et métiers (France) (1988).Louis de Broglie que nous avons connu. Fondation Louis de Broglie, Conservatoire national des arts et métiers.
  24. ^The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective. New York: Wiley-Interscience, 1974.ISBN 0-471-43958-4
  25. ^J. Mehra. (2001). "Louis de Broglie and the phase waves associated with matter". In J. Mehra. (ed.).The Golden Age of Theoretical Physics. World Scientific. pp. 546–570.
  26. ^"Membres de l'Académie des sciences depuis sa création: Louis de Broglie Ondes et quanta"(PDF).academie-sciences.fr (in French). 1923.
  27. ^Max JammerThe Conceptual Development of Quantum Mechanics. New York: McGraw-Hill, 1966 2nd ed: New York: American Institute of Physics, 1989.ISBN 0-88318-617-9. Olivier Darrigol, "Strangeness and soundness in Louis de Broglie's early works",Physis, 30 (1993): 303–372.
  28. ^Moore, Walter John (2015).Schrödinger: life and thought. Canto classics. Cambridge, United Kingdom: Cambridge University Press. p. 187.ISBN 978-1-107-56991-1.
  29. ^Hawking, Stephen, ed. (2011). "Quantization as an Eigenvalue Problem, Parts I-IV, in Chapter 3".The dreams that stuff is made of: the most astounding papers on quantum physics--and how they shook the scientific world. Philadelphia, PA: Running Press.ISBN 978-0-7624-3434-3.
  30. ^See for example the description of de Broglie's view in: David Bohm, Basil Hiley:The de Broglie pilot wave theory and the further development and new insights arising out of it, Foundations of Physics, volume 12, number 10, 1982, Appendix: On the background of the papers on trajectories interpretation, by D. Bohm, (PDFArchived 19 August 2011 at theWayback Machine)
  31. ^D. Hestenes, October 1990, The Zitterbewegung interpretation of quantum mechanics, Foundations of Physics, vol. 20, no. 10, pp. 1213–1232
  32. ^See for example G.R. Osche,Electron channeling resonance and de Broglie's internal clock, Annales de la Fondation Louis de Broglie, vol. 36, 2001, pp. 61–71 (full text)
  33. ^Catillon, Foundations of Physics, July 2001, vol. 38, no. 7, pp. 659–664
  34. ^Pryce, Maurice Henry Lecorney; null, null; Dirac, Paul Adrien Maurice; null, null (1997)."On the neutrino theory of light".Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.165 (921):247–271.doi:10.1098/rspa.1938.0058.
  35. ^Perkins, W. A. (1965)."Neutrino Theory of Photons".Physical Review.137 (5B):B1291 –B1301.Bibcode:1965PhRv..137.1291P.doi:10.1103/PhysRev.137.B1291.
  36. ^"APS Member History".search.amphilsoc.org. Retrieved10 May 2023.
  37. ^"Duc L. De Broglie".www.nasonline.org. Retrieved10 May 2023.
  38. ^Abragam, A. (1988). "Louis Victor Pierre Raymond de Broglie. 15 August 1892-19 March 1987".Biographical Memoirs of Fellows of the Royal Society.34:22–26.doi:10.1098/rsbm.1988.0002.JSTOR 770045.
  39. ^"Louis Victor Pierre Raymond de Broglie".American Academy of Arts & Sciences. 9 February 2023. Retrieved10 May 2023.
  40. ^"Review ofEinstein by Louis de Broglie and others".Bulletin of the Atomic Scientists.36 (3): 50. March 1980.

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