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1

Rechenberg, H., and Georges Lochak. "Louis de Broglie zum Gedenken/Louis de Broglie." Physik Journal 43, no. 6 (June 1987): 170–71. http://dx.doi.org/10.1002/phbl.19870430613.

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2

López, Carlos. "De Broglie Waves." OALib 07, no. 02 (2020): 1–8. http://dx.doi.org/10.4236/oalib.1106100.

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3

Pestre, Dominique. "Louis de Broglie: Un itinéraire scientifique. Louis de Broglie , Georges Lochak." Isis 79, no. 4 (December 1988): 740–41. http://dx.doi.org/10.1086/354911.

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4

George, Thomas F. "De Broglie-wave lens." Optical Engineering 47, no. 2 (February 1, 2008): 028001. http://dx.doi.org/10.1117/1.2844696.

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5

Jacobson, Joseph, Gunnar Björk, Isaac Chuang, and Yoshihisa Yamamoto. "Photonic de Broglie Waves." Physical Review Letters 74, no. 24 (June 12, 1995): 4835–38. http://dx.doi.org/10.1103/physrevlett.74.4835.

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6

Barros, Alexsandro De Almeida, and Marcos Antonio Barros. "“Uma teoria experimental dos quanta de luz” de Louis de Broglie: uma tradução comentada." Revista Sustinere 6, no. 1 (July 19, 2018): 175–200. http://dx.doi.org/10.12957/sustinere.2018.31732.

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Este artigo apresenta e discute uma das comunicações escritas em língua inglesa, enviada a Philosophical Magazine pelo físico francês Louis de Broglie, em 1924, intitulada “A tentative theory of light quanta”. No referido trabalho, de Broglie traz uma síntese das ideias tratadas em outros três artigos publicados em francês e propõe a elaboração de uma teoria dualística para a luz, enquanto explicação para muitos fenômenos que não podiam ser corretamente explicados pelas teorias ondulatória e corpuscular, se isoladas. Além de discutir resultados já conhecidos pela comunidade científica de sua época, os trabalhos de de Broglie apresentam ideias totalmente originais, embora já contivessem conceitos que são cruciais para a explicação de muitos fenômenos conhecidos atualmente (a exemplo do laser). Acreditamos que este material possa servir de suporte para a discussão dos principais aspectos dos trabalhos iniciais de de Broglie, haja vista que algumas de suas ideias são ainda adotadas, atualmente, e constituem parte dos conteúdos de física moderna e contemporânea.
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7

Bauer, M. "de Broglie clock, electron channeling, and time in quantum mechanics." Canadian Journal of Physics 97, no. 1 (January 2019): 37–41. http://dx.doi.org/10.1139/cjp-2017-0571.

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De Broglie’s association of a wave to particles is a fundamental concept in the quantum mechanical description of nature. The wave oscillation is referred to alternatively as the “de Broglie clock”, the “Compton clock”, or the “de Broglie periodic phenomenon”. In the present paper it is shown that Dirac’s relativistic quantum mechanics, complemented with the dynamical time operator recently introduced, provides a consistent theoretical description of: (i) the generation of the de Broglie wave through Lorentz boosts; and (ii) the characteristics of the resonance observed in electron channeling through thin crystals as responding to both the periodicity derived from the adjustment of the de Broglie period to the crystal interatomic distance (resonance energy) and the periodicity of the predicted trembling motion (Zitterbewegung). One can conclude that the channeling experiments provide the first direct evidence of the electron Zitterbewegung, and that the de Broglie period is an intrinsic property of matter arising from a self-adjoint dynamical time operator.
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8

Smorodinskii, Ya A., and T. B. Romanovskaya. "Louis de Broglie (1892–1987)." Uspekhi Fizicheskih Nauk 156, no. 12 (1988): 753. http://dx.doi.org/10.3367/ufnr.0156.198812e.0753.

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9

d'Espagnat, Bernard. "Louis de Broglie (1892–1987)." Nature 327, no. 6120 (May 1987): 283. http://dx.doi.org/10.1038/327283a0.

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10

Smorodinskiĭ, Ya A., and T. B. Romanovskaya. "Louis de Broglie (1892–1987)." Soviet Physics Uspekhi 31, no. 12 (December 31, 1988): 1080–84. http://dx.doi.org/10.1070/pu1988v031n12abeh005661.

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11

Haslett, J. W. "Textbook misquotations of de Broglie." American Journal of Physics 60, no. 7 (July 1992): 583. http://dx.doi.org/10.1119/1.17106.

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12

Whitaker, M. A. B. "Bethe, Bell and De Broglie." American Journal of Physics 63, no. 10 (October 1995): 873. http://dx.doi.org/10.1119/1.17783.

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13

Vallée, Robert. "Louis de Broglie and Cybernetics." Kybernetes 19, no. 2 (February 1990): 32–33. http://dx.doi.org/10.1108/eb005840.

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14

Strnad, J., and W. Kuhn. "On the de Broglie waves." European Journal of Physics 6, no. 3 (July 1, 1985): 176–79. http://dx.doi.org/10.1088/0143-0807/6/3/009.

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15

Schewe, Phil F. "The photonic de Broglie wavelength." Physics Today 56, no. 1 (January 2003): 9. http://dx.doi.org/10.1063/1.4796891.

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16

Guinier, A. "Louis de Broglie, 1892–1987." Journal of Applied Crystallography 20, no. 6 (December 1, 1987): 451–52. http://dx.doi.org/10.1107/s0021889887085984.

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17

Barnett, Stephen M., Nobuyuki Imoto, and Bruno Huttner. "Photonic de broglie wave interferometers." Journal of Modern Optics 45, no. 11 (November 1998): 2217–32. http://dx.doi.org/10.1080/09500349808231234.

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18

Lochak, Georges. "Louis de Broglie (1892?1987)." Foundations of Physics 17, no. 10 (October 1987): 967–70. http://dx.doi.org/10.1007/bf00938006.

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19

Baylis, William E. "De Broglie waves as an effect of clock desynchronization." Canadian Journal of Physics 85, no. 12 (December 1, 2007): 1317–23. http://dx.doi.org/10.1139/p07-121.

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De Broglie waves are a simple consequence of special relativity applied to the complex-phase oscillations of stationary states. As de Broglie showed in his doctoral thesis, the synchronized oscillations of an extended system at rest, even a classical one, become de Broglie-like waves when boosted to finite velocity. The waves illustrate the well-known but seldom demonstrated relativistic effect of clock desynchroniation (or dephasing) in moving frames. Although common manifestations of stationary-state oscillations in interference experiments are sensitive only to energy differences, de Broglie wavelengths are inversely proportional to rest-frame oscillation frequency, and their observed values require that the oscillation frequencies are proportional to the the total absolute energy, including the rest component mc2. PACS Nos.: 03.65.Ta, 03.30.+p, 01.65.+g
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20

Sato, Masanori. "De Broglie waves, the Schrödinger equation, and relativity. I. Exclusion of the rest mass energy in the dispersion relation." Physics Essays 33, no. 1 (March 4, 2020): 96–98. http://dx.doi.org/10.4006/0836-1398-33.1.96.

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The difference between de Broglie waves and the Schrödinger equation is the rest mass. The dispersion relation of de Broglie waves includes the rest mass, but the Schrödinger equation does not. Synchrotron radiation is when de Broglie waves shake off virtual photons and emit real photons. It also shows that synchrotron radiation is not compatible with relativity.
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21

Shuler, Robert L. "Common Pedagogical Issues with De Broglie Waves: Moving Double Slits, Composite Mass, and Clock Synchronization." Physics Research International 2015 (December 1, 2015): 1–8. http://dx.doi.org/10.1155/2015/895134.

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This paper addresses gaps identified in pedagogical studies of how misunderstanding of De Broglie waves affects later coursework and presents a heuristic for understanding the De Broglie frequency of composite. De Broglie’s little known derivation is reviewed with a new illustration based on his description. Simple techniques for reference frame independent analysis of a moving double slit electron interference experiment are not previously found in any literature and cement the concepts. Points of similarity and difference between De Broglie and Schrödinger waves are explained. The necessity of momentum, energy, and wavelength changes in the electrons in order for them to be vertically displaced in their own reference frame is shown to be required to make the double slit analysis work. A relativistic kinematic analysis of De Broglie frequency is provided showing how the higher De Broglie frequency of moving particles is consistent with Special Relativity and time dilation and that it demonstrates a natural system which obeys Einstein’s clock synchronization convention of simultaneity and no other. Students will be better prepared to identify practical approaches to solving problems and to think about fundamental questions.
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22

Brill, Michael H. "De Broglie waves meet Schrödinger's equation." Physics Essays 26, no. 4 (December 30, 2013): 574–76. http://dx.doi.org/10.4006/0836-1398-26.4.574.

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23

Vigier, Jean-Pierre. "Louis de Broglie et Albert Einstein." Raison présente 84, no. 1 (1987): 101–7. http://dx.doi.org/10.3406/raipr.1987.2636.

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24

Cahn, S. B., A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky. "Time-Domain de Broglie Wave Interferometry." Physical Review Letters 79, no. 5 (August 4, 1997): 784–87. http://dx.doi.org/10.1103/physrevlett.79.784.

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25

Krutzik, Markus. "Von de Broglie zur Dunklen Energie." Physik in unserer Zeit 49, no. 5 (September 2018): 211. http://dx.doi.org/10.1002/piuz.201870502.

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26

Talantsev, E. F. "Critical de Broglie wavelength in superconductors." Modern Physics Letters B 32, no. 09 (March 30, 2018): 1850114. http://dx.doi.org/10.1142/s0217984918501142.

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There are growing numbers of experimental evidences that the self-field critical currents, [Formula: see text], are a new instructive tool to investigate fundamental properties of superconductors ranging from atomically thin films [M. Liao et al., Nat. Phys. 6 (2018), https://doi.org/10.1038/s41567-017-0031-6 ; E. F. Talantsev et al., 2D Mater. 4 (2017) 025072; A. Fete et al., Appl. Phys. Lett. 109 (2016) 192601] to millimeter-scale samples [E. F. Talantsev et al., Sci. Rep. 7 (2017) 10010]. The basic empirical equation which quantitatively accurately described experimental [Formula: see text] was proposed by Talantsev and Tallon [Nat. Commun. 6 (2015) 7820] and it was the relevant critical field (i.e. thermodynamic field, [Formula: see text], for type-I and lower critical field, [Formula: see text], for type-II superconductors) divided by the London penetration depth, [Formula: see text]. In this paper, we report new findings relating to this empirical equation. It is that the critical wavelength of the de Broglie wave, [Formula: see text], of the superconducting charge carrier which within a numerical pre-factor is equal to the largest of two characteristic lengths of Ginzburg–Landau theory, i.e. the coherence length, [Formula: see text], for type-I superconductors or the London penetration depth, [Formula: see text], for type-II superconductors. We also formulate a microscopic criterion for the onset of dissipative transport current flow: [Formula: see text], where [Formula: see text] is the charge carrier momentum, [Formula: see text] is Planck’s constant and the inequality sign “[Formula: see text]” is reserved for the dissipation-free flow.
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27

Man’ko, Vladimir I., and Lyubov A. Markovich. "Symplectic Tomography of De Broglie Wave." Journal of Russian Laser Research 38, no. 6 (November 2017): 507–15. http://dx.doi.org/10.1007/s10946-017-9674-0.

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28

Juffmann, Thomas, Stefan Nimmrichter, Markus Arndt, Herbert Gleiter, and Klaus Hornberger. "New Prospects for de Broglie Interferometry." Foundations of Physics 42, no. 1 (November 20, 2010): 98–110. http://dx.doi.org/10.1007/s10701-010-9520-5.

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29

Lepore, Vito Luigi. "Homodyne detection of de Broglie waves." Foundations of Physics Letters 5, no. 5 (October 1992): 469–78. http://dx.doi.org/10.1007/bf00690427.

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30

Ghins, Michel. "Are de Broglie and Bohm right?" Metascience 27, no. 1 (October 9, 2017): 91–94. http://dx.doi.org/10.1007/s11016-017-0261-3.

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31

Holland, P. R. "Geometry of dislocated de Broglie waves." Foundations of Physics 17, no. 4 (April 1987): 345–63. http://dx.doi.org/10.1007/bf00733373.

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32

Fonseca, E. J. S., Zoltan Paulinia, P. Nussenzveig, C. H. Monkena, and S. Padua. "Nonlocal de Broglie Wavelength of a Two-Photon System." Zeitschrift für Naturforschung A 56, no. 1-2 (February 1, 2001): 191–96. http://dx.doi.org/10.1515/zna-2001-0132.

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AbstractWe show that it is possible to associate a de Broglie wavelength to a composite system even when the constituent particles are separated spatially. The nonlocal de Broglie wavelength (A /2) of a two-photon system separated spatially is measured with an appropriate detection system. The two-photon system is prepared in an entangled state in space-momentum variables. - Pacs: 42.50.-p, 42.50.Ar
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33

Zhou, Yu, Tao Peng, Hui Chen, Jianbin Liu, and Yanhua Shih. "Towards Non-Degenerate Quantum Lithography." Applied Sciences 8, no. 8 (August 3, 2018): 1292. http://dx.doi.org/10.3390/app8081292.

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The photonic de Broglie wavelength of a non-degenerate entangled photon pair is measured by using a Young’s double slit interferometer, which proves that the non-degenerate entangled photon pairs have the potential to be used in quantum lithography. Experimental results show that the de Broglie wavelength of non-degenerate biphotons is well defined and its wavelength is neither the wavelength of the signal photon, nor the wavelength of the idler photon. According to the de Broglie equation, its wavelength corresponds to the momentum of the biphoton, which equals the sum of the momenta of signal and idler photons. The non-degenerate ghost interference/diffraction is also observed in these experiments.
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34

López, Carlos. "How to Detect Quantum (de Broglie) Waves." OALib 07, no. 09 (2020): 1–5. http://dx.doi.org/10.4236/oalib.1106741.

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35

Fujita, J., and F. Shimizu. "Atom manipulation using atomic de Broglie waves." Materials Science and Engineering: B 96, no. 2 (November 2002): 159–63. http://dx.doi.org/10.1016/s0921-5107(02)00310-0.

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36

Henry, Joan A. "The de Broglie relationship—Fact and fiction." American Journal of Physics 60, no. 12 (December 1992): 1065. http://dx.doi.org/10.1119/1.16950.

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37

Kobe, Donald H. "Quantum power in de Broglie–Bohm theory." Journal of Physics A: Mathematical and Theoretical 40, no. 19 (April 24, 2007): 5155–62. http://dx.doi.org/10.1088/1751-8113/40/19/015.

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38

Metcalf, H. "Dark States and De Broglie Wave Optics." Acta Physica Polonica A 93, no. 1 (January 1998): 147–57. http://dx.doi.org/10.12693/aphyspola.93.147.

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39

Fonseca, E. J. S., C. H. Monken, and S. Pádua. "Measurement of the Photonic de Broglie Wavelength." Fortschritte der Physik 48, no. 5-7 (May 2000): 517–21. http://dx.doi.org/10.1002/(sici)1521-3978(200005)48:5/7<517::aid-prop517>3.0.co;2-k.

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40

Steane, A., P. Szriftgiser, P. Desbiolles, and J. Dalibard. "Phase Modulation of Atomic de Broglie Waves." Physical Review Letters 74, no. 25 (June 19, 1995): 4972–75. http://dx.doi.org/10.1103/physrevlett.74.4972.

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41

Contopoulos, G., N. Delis, and C. Efthymiopoulos. "Order in de Broglie–Bohm quantum mechanics." Journal of Physics A: Mathematical and Theoretical 45, no. 16 (April 3, 2012): 165301. http://dx.doi.org/10.1088/1751-8113/45/16/165301.

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42

Davidson, Michael W. "Pioneers in Optics: Louis de Broglie and Edwin Herbert Land." Microscopy Today 21, no. 3 (May 2013): 44–46. http://dx.doi.org/10.1017/s1551929513000424.

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In the early twentieth century, the long standing argument about whether the character of light was particle-based or wavelike was finally coming to an end as the scientists of the day began to accept that light could assume a dual nature. The possibility that such a duality might apply to matter as well as light was first proposed by physicist Louis de Broglie. Born in Dieppe, France, de Broglie studied in Paris and was descended from members of the French nobility. In his youth, he considered a career as a diplomat but later turned to science and pursued the study of theoretical physics. His brother, Maurice, who had also decided to become a physicist and made many advances in the study of X rays, reportedly had a considerable influence on de Broglie and was the first to introduce him to the work of Albert Einstein and Max Planck.
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43

Costa De Beauregard, O. "A l'occasion du 90e anniversaire de Louis de Broglie." Revue d'histoire des sciences 38, no. 3 (1985): 365–67. http://dx.doi.org/10.3406/rhs.1985.4013.

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44

Stavek, Jiri. "Wilhelm Wien’s Photons Creating the BohEmian Pilot Wave for the Guiding of the Individual Huygens - de Broglie Particles on the Helical Path Governed by the Newton - Bohm Evolute (the Bohmian Pilot Wave) through the Young - Feynman Double - Slit Barrier." Applied Physics Research 11, no. 5 (September 30, 2019): 10. http://dx.doi.org/10.5539/apr.v11n5p10.

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In our approach we have combined knowledge of Old Masters (working in this field before the year 1905), New Masters (working in this field after the year 1905) and Dissidents under the guidance of Louis de Broglie and David Bohm. In our model the quantum particle is represented as the Huygens-de Broglie&rsquo;s particle on the helical path (full wave) guided by the Newton-Bohm entangled helical evolute (Bohmian Pilot Wave). These individual Huygens - de Broglie particles in the Young - Feynman double - slit experiment react with Wilhelm Wien&rsquo;s photons that are always present inside of the apparatus (Wien&rsquo;s displacement law). Wilhelm Wien&rsquo;s photons form collectively the Wien filter guiding the Huygens - de Broglie particles through the double - slit barrier towards a detector (BohEmian Pilot Wave). The interplay of those events creates the observed interference pattern. In the very well-known formula describing the intensity of double-slit diffraction patterns we have newly introduced the concept curvature &kappa; of the Huygens - de Broglie particle and thus giving a physical interpretation for the Newton - Bohm guiding wave (the Bohmian Pilot Wave): for photons &kappa; = &pi;/&lambda;, for electrons &kappa; = 2&pi;/&lambda;. Moreover, we have introduced into that formula the expression &lambda;max from the Wien&rsquo;s displacement law to describe geometry of the double - slit barrier. We propose to modify the value &lambda;max by the change of the system temperature. There is a second experimental possibility - we can insert into those slits filters to remove Wien&rsquo;s photons while the Huygens - de Broglie particles continue towards a detector - we should observe the particle behavior. The similar situation might occur in the Mach - Zehnder interferometer. In this case the individual Huygens - de Broglie particle reacts in the first beam splitter with the Wien photon: the Huygens - de Broglie particle goes through one path while the Wien photon goes through the second path. In the second beam splitter they interact again and create the interference pattern on one detector. We can experimentally modify the resulting interference pattern in the Mach - Zehnder interferometer - by the temperature change of the system or by inserting filters to remove Wien&rsquo;s photons from one or both paths. Can it be that Nature cleverly creates those interference patterns while the Bohmian pilot wave and the BohEmian pilot wave are hidden in plain sight? We want to pass this concept into the hands of Readers of this Journal better educated in the Mathematics and Physics.
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45

Wagner, Fernando Da Cunha. "Resenha do livro "De Broglie” de José Maria Filardo Bassalo e Francisco Caruso." Caderno Brasileiro de Ensino de Física 33, no. 2 (September 8, 2016): 732. http://dx.doi.org/10.5007/2175-7941.2016v33n2p732.

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http://dx.doi.org/10.5007/2175-7941.2016v33n2p732Resenha do livro "De Broglie” de José Maria Filardo Bassalo e Francisco CarusoEditora Livraria da Física, São Paulo, 2015, 1a edição, 94 pISBN: 9788578613372
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46

Hatifi, Mohamed, Ralph Willox, Samuel Colin, and Thomas Durt. "Bouncing Oil Droplets, de Broglie’s Quantum Thermostat, and Convergence to Equilibrium." Entropy 20, no. 10 (October 11, 2018): 780. http://dx.doi.org/10.3390/e20100780.

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Recently, the properties of bouncing oil droplets, also known as “walkers,” have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behavior. They indeed constitute a macroscopic realization of wave-particle duality, in the sense that their trajectories are guided by a self-generated surrounding wave. The aim of this paper is to try to describe walker phenomenology in terms of de Broglie–Bohm dynamics and of a stochastic version thereof. In particular, we first study how a stochastic modification of the de Broglie pilot-wave theory, à la Nelson, affects the process of relaxation to quantum equilibrium, and we prove an H-theorem for the relaxation to quantum equilibrium under Nelson-type dynamics. We then compare the onset of equilibrium in the stochastic and the de Broglie–Bohm approaches and we propose some simple experiments by which one can test the applicability of our theory to the context of bouncing oil droplets. Finally, we compare our theory to actual observations of walker behavior in a 2D harmonic potential well.
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47

Hill, James M. "A review of de Broglie particle–wave mechanical systems." Mathematics and Mechanics of Solids 25, no. 10 (June 7, 2020): 1763–77. http://dx.doi.org/10.1177/1081286520917201.

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The existence of the so-called ‘dark’ issues of mechanics implies that our present accounting for mass and energy is incorrect in terms of applicability on a cosmological scale, and the question arises as to where the difficulty might lie. The phenomenon of quantum entanglement indicates that systems of particles exist that individually display certain characteristics, while collectively the same characteristic is absent simply because it has cancelled out between individual particles. It may therefore be necessary to develop theoretical frameworks in which long-held conservation beliefs do not necessarily always apply. The present paper summarises the formulation described in earlier papers (Hill, JM. On the formal origin of dark energy. Z Angew Math Phys 2018; 69:133-145; Hill, JM. Some further comments on special relativity and dark energy. Z Angew Math Phys 2019; 70: 5–14; Hill, JM. Special relativity, de Broglie waves, dark energy and quantum mechanics. Z Angew Math Phys 2019; 70: 131–153.), which provides a framework that allows exceptions to the law that matter cannot be created or destroyed. In these papers, it is proposed that dark energy arises from conventional mechanical theory, neglecting the work done in the direction of time and consequently neglecting the de Broglie wave energy [Formula: see text]. These papers develop expressions for the de Broglie wave energy [Formula: see text] by making a distinction between particle energy [Formula: see text] and the total work done by the particle [Formula: see text], that which accumulates from both a spatial physical force [Formula: see text] and a force [Formula: see text] in the direction of time. In any experiment, either particles or de Broglie waves are reported, so that only one of [Formula: see text] or [Formula: see text] is physically measured, and particles appear for [Formula: see text] and de Broglie waves occur for [Formula: see text], but in either event both a measurable and an immeasurable energy exists. Conventional quantum mechanics operates under circumstances such that [Formula: see text] vanishes and [Formula: see text] becomes purely imaginary. If both [Formula: see text] and [Formula: see text] are generated as the gradient of a potential, the total particle energy is necessarily conserved in the conventional manner.
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48

Vysikaylo, P. I., N. V. Samsonenko, and M. V. Semin. "De Broglie wave in vacuum, matter and nanostructures." Journal of Physics: Conference Series 1560 (June 2020): 012006. http://dx.doi.org/10.1088/1742-6596/1560/1/012006.

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49

Silva, P. R. "A New Interpretation of the de Broglie Frequency?" Physics Essays 10, no. 4 (December 1997): 628–32. http://dx.doi.org/10.4006/1.3028741.

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50

Newburgh, Ronald G. "The de Broglie Relations: Lorentz Invariance and Photons." Physics Essays 1, no. 2 (June 1, 1988): 102–8. http://dx.doi.org/10.4006/1.3036441.

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