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Wave–particle duality

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Before proceeding further, it is critical to introduce some definitions of waves and particles both in a classical sense and in quantum mechanics. Waves and particles are two very different models for physical systems, each with an exceptionally large range of application. Classical waves obey the
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The first beam-splitter mirror acts like double slits, but in the interferometer case we can remove the second beam splitter. Then the beam heading down ends up in output port 1: any photon particles on this path gets counted in that port. The beam going across the top ends up on output port 2. In
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is considered to be a particle-like property, for instance a spinning top. However, light waves can have angular momentum when they form a vortex, as illustrated in the Figure. Electron waves with angular momentum have also been produced, with up to a thousand angular momentum quanta. These matter
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Electrons from the source hit a wall with two thin slits. A mask behind the slits can expose either one or open to expose both slits. The results for high electron intensity are shown on the right, first for each slit individually, then with both slits open. With either slit open there is a smooth
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In a "which way" experiment, particle detectors are placed at the slits to determine which slit the electron traveled through. When these detectors are inserted, quantum mechanics predicts that the interference pattern disappears because the detected part of the electron wave has changed (loss of
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Having observed wave behavior, now change the experiment, lowering the intensity of the electron source until only one or two are detected per second, appearing as individual particles, dots in the video. As shown in the movie clip below, the dots on the detector seem at first to be random. After
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to fully describe the behavior of quantum objects. During the 19th and early 20th centuries, light was found to behave as a wave then later discovered to have a particulate behavior, whereas electrons behaved like particles in early experiments then later discovered to have wavelike behavior. The
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and Alexander Reid at Cambridge University scattered electrons through thin metal films and observed concentric diffraction rings. Alexander Reid, who was Thomson's graduate student, performed the first experiments, but he died soon after in a motorcycle accident and is rarely mentioned. These
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approach as the positions were systematically different; the approach of Bethe, which includes the refraction due to the average potential, yielded more accurate results. Davisson and Thomson were awarded the Nobel Prize in 1937 for experimental verification of wave property of electrons by
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Each output port has a camera to record the results. The two beams show interference characteristic of wave propagation. If the laser intensity is turned sufficiently low, individual dots appear on the cameras, building up the pattern as in the electron example.
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Experimental electron double slit diffraction pattern. Across the middle of the image at the top the intensity alternates from high to low showing interference in the signal from the two slits. Bottom: movie of the pattern build up dot by dot.
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suggested that the energy of the light must occur a finite number of energy quanta. He postulated that electrons can receive energy from an electromagnetic field only in discrete units (quanta or photons): an amount of
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The experiment shows wave interference revealed a single particle at a time -- quantum mechanical electrons display both wave and particle behavior. Similar results have been shown for atoms and even large molecules.
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in the 1930s using beams of helium atoms and hydrogen molecules. These experiments further verified that wave behavior is not limited to electrons and is a general property of matter on a microscopic scale.
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from 1922 to 1924 demonstrating the momentum of light. The experimental evidence of particle-like momentum and energy seemingly contradicted the earlier work demonstrating wave-like interference of light.
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and that electrons and all matter could be considered as waves. He merged the idea of thinking about them as particles, and of thinking of them as waves. He proposed that particles are bundles of waves
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have been made and many have been converted into experiments and tried out. Every single one shows the same result: as soon as electron trajectories are detected, interference disappears.
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Both discrete (quantized) energies and also momentum are, classically, particle attributes. There are many other examples where photons display particle-type properties, for instance in
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gave a talk in an Oxford meeting about using the electron diffraction experiments to confirm the wave–particle duality of electrons. In his talk, Born cited experimental data from
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Tavabi, A. H.; Rosi, P.; Roncaglia, A.; Rotunno, E.; Beleggia, M.; Lu, P.-H.; Belsito, L.; Pozzi, G.; Frabboni, S.; Tiemeijer, P.; Dunin-Borkowski, R. E.; Grillo, V. (2022).
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Left half: schematic setup for electron double-slit experiment with masking; inset micrographs of slits and mask; Right half: results for slit 1, slit 2 and both slits open.
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in 1923. It happened that Davisson also attended that talk. Davisson returned to his lab in the US to switch his experimental focus to test the wave property of electrons.
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The electron double slit experiment is a textbook demonstration of wave-particle duality. A modern version of the experiment is shown schematically in the figure below.
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waves will diffract and interfere, while simultaneously having particle-like angular momentum so they will interact with magnetic fields, similar to a current loop.
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either case the counts will track the photon trajectories. However, as soon as the second beam splitter is removed the interference pattern disappears.
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Quantum systems obey wave equations that predict particle probability distributions. These particles are associated with discrete values called
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also with discrete energies for photons. These both indicate particle behavior. Despite confirmation by various experimental observations, the
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among others had shown that free electrons had particle properties, for instance, the measurement of their mass by Thomson in 1897. In 1924,
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While electrons were thought to be particles until their wave properties were discovered; for photons it was the opposite. In 1887,
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Some experiments on quantum systems show wave-like interference and diffraction; some experiments show particle-like collisions.
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intensity variation due to diffraction. When both slits are open the intensity oscillates, characteristic of wave interference.
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A laser beam along the input port splits at a half-silvered mirror. Part of the beam continues straight, passes though a glass
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Line trace for a two-slit electron interference pattern. Compare to a slice through the image of the water wave pattern above.
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entities exhibit particle or wave properties according to the experimental circumstances. It expresses the inability of the
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A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century
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The collected papers of Albert Einstein. 3: The Swiss years: writings, 1909 - 1911: [English translation]
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Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character
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developed the wave equation of motion for electrons. This rapidly became part of what was called by Schrödinger
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heuristically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged
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where the momentum is used to slow down (cool) atoms. These are a different aspect of wave-particle duality.
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experiments were rapidly followed by the first non-relativistic diffraction model for electrons by
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some time a pattern emerges, eventually forming an alternating sequence of light and dark bands.
1207:: particle models work across a huge scale. Unlike waves, particles do not exhibit interference. 769: 487: 395: 5087: 4635: 1649: 1106: 1071: 445: 343: 109: 5691: 5599: 5571: 5474: 5333: 4998: 4773: 4753: 4678: 4546: 4217: 3554: 2866:"Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" 2544: 1510: 1329: 774: 492: 320: 290: 253: 4589: 1490: 1417:
observed that when light with sufficient frequency hits a metallic surface, the surface emits
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The contradictory evidence from electrons arrived in the opposite order. Many experiments by
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in 1819, validated Huygen's wave models. However, the wave model was challenged in 1901 by
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A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926
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In 1927, the wave nature of electrons was empirically confirmed by two experiments. The
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Following de Broglie's proposal of wave–particle duality of electrons, in 1925 to 1926,
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comes in from the left, collides with a target at rest, and a new photon of wavelength
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discovered that the maximum possible energy of an ejected electron is unrelated to its
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diffraction experiments. Similar crystal diffraction experiments were carried out by
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Wheaton, Bruce R. (1978). "Philipp Lenard and the Photoelectric Effect, 1889-1911".
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The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
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Allen, L.; Beijersbergen, M. W.; Spreeuw, R. J. C.; Woerdman, J. P. (1992).
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Bach, Roger; Pope, Damian; Liou, Sy-Hwang; Batelaan, Herman (2013-03-13).
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in a cavity that contained black-body radiation could only change its
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theory (as it came to be called later) remained controversial until
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Both interference and trajectories are observed in quantum systems
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Ma, Xiao-song; Kofler, Johannes; Zeilinger, Anton (2016-03-03).
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concept of duality arose to name these seeming contradictions.
2000:"An Undulatory Theory of the Mechanics of Atoms and Molecules" 987:
theory (as it came to be called) remained controversial until
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in water due to two sources marked as red points on the left.
1184: 3091:"Delayed-choice gedanken experiments and their realizations" 1323: 3948: 3880: 3840: 3416: 3411: 2968: 2093:"The scattering of electrons by a single crystal of nickel" 971:, that was proportional to the frequency of its associated 906: 3031: 1837:"Ueber das Gesetz der Energieverteilung im Normalspectrum" 1825:(Leiden, Netherlands: Pieter van der Aa, 1690), Chapter 1. 1245:
for a mass thrown at an angle of 70°, at different speeds.
2676:"Testing the limits of quantum mechanical superpositions" 2438:"The diffraction of cathode rays by thin celluloid films" 1642:
A simple example of these "which way" experiments uses a
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Classical waves interfere. Particles follow trajectories.
1979:(English translation by A.F. Kracklauer, 2004. ed.) 1708:
Pages displaying short descriptions of redirect targets
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Pages displaying short descriptions of redirect targets
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from 1922 to 1924 demonstrating the momentum of light.
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Die Grundlagen der Einsteinschen Relativitäts-Theorie
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Schneider, Mark B.; LaPuma, Indhira A. (2002-03-01).
2971:"Production and application of electron vortex beams" 1706: – Number of quantum physics thought experiments 1538: 1513: 1493: 1457: 39: 2969:
Verbeeck, J.; Tian, H.; Schattschneider, P. (2010).
2608: 1776: 3146: 3144: 3142: 2545:"Theorie der Beugung von Elektronen an Kristallen" 1591:, where sunlight could propel a space vehicle and 1544: 1524: 1499: 1472: 999: 100: 5344:Investigations on the Theory of Brownian Movement 3088: 3082: 2192:"Diffraction of Electrons by a Crystal of Nickel" 2143:"Diffraction of Electrons by a Crystal of Nickel" 1390: 918: 5817: 2244:"Reflection of Electrons by a Crystal of Nickel" 1598: 1122: 3150: 3139: 2673: 2318:Proceedings of the National Academy of Sciences 2248:Proceedings of the National Academy of Sciences 1092:at Bell Labs measured electrons scattered from 5351:Relativity: The Special and the General Theory 2499:The British Journal for the History of Science 2311: 2241: 2189: 2140: 1798:. Vol. 3. 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(1927). 43: 5798: 5797: 5534:Einstein Prize for Laser Science 5123: 5122: 4330: 4223:Timeline of particle discoveries 3240: 1653:Interferometer schematic diagram 1368: 1357: 1264: 1252: 1234: 1219: 931:took an opposing wave approach. 5579:Einstein: His Life and Universe 3025: 2962: 2923: 2747: 2667: 2575: 2486: 2429: 2372: 2183: 2077: 2038: 1796:The Feynman Lectures on Physics 1690: – Quantum physics concept 1399:Photoelectric effect in a solid 1000:Wave-particle duality of matter 5201:Mass–energy equivalence (E=mc) 5072:Relativistic quantum mechanics 1977:Foundation of Louis de Broglie 1922: 1861: 1828: 1812: 1694:Einstein's thought experiments 1613:Focused Laguerre-Gaussian beam 1391:Observing photons as particles 923:In the late 17th century, Sir 919:Wave-particle duality of light 556:Relativistic quantum mechanics 88: 81: 62: 1: 5050:Quantum statistical mechanics 4827:Quantum differential calculus 4749:Delayed-choice quantum eraser 4532:Symmetry in quantum mechanics 2645:10.1088/1367-2630/15/3/033018 2621:(3). 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T. (1910). 2511:10.1017/S0007087410000026 1970:"On the Theory of Quanta" 1947:10.1080/14786449708621070 1868:Einstein, Albert (1993). 1688:Complementarity (physics) 1525:{\displaystyle \lambda '} 1159:Classical particles obey 1026:introduced his theory of 5750:Albert Einstein Archives 5680:Bernhard Caesar Einstein 5427:Relics: Einstein's Brain 5375:The Evolution of Physics 5256:Bose–Einstein statistics 5251:Bose–Einstein condensate 5231:Einstein field equations 4979:Quantum machine learning 4959:Quantum key distribution 4949:Quantum image processing 4939:Quantum error correction 4789:Wheeler's delayed choice 4256:mathematical formulation 3851:Eta and eta prime mesons 2948:10.1103/PhysRevA.45.8185 2893:10.1002/andp.19053220607 2743:. Longman, Green and Co. 2569:10.1002/andp.19283921704 2436:Reid, Alexander (1928). 1998:Schrödinger, E. (1926). 1854:10.1002/andp.19013090310 1745:Messiah, Albert (1966). 1500:{\displaystyle \lambda } 1441:that was related to the 1167:and extent; they follow 1030:waves in his PhD thesis 967:in a minimal increment, 937:interference experiments 601:Quantum machine learning 354:Wheeler's delayed-choice 5760:Einstein Papers Project 5276:Einstein–de Haas effect 4895:Quantum finite automata 3918:Double-charm tetraquark 3219:"Wave–particle duality" 3199:"Wave–Particle Duality" 3038:Applied Physics Letters 2493:Navarro, Jaume (2010). 2024:10.1103/PhysRev.28.1049 1929:Thomson, J. J. (1897). 1545:{\displaystyle \theta } 1487:A photon of wavelength 1300:for properties such as 1279:acting like a particle. 311:Leggett–Garg inequality 5692:Thomas Martin Einstein 5600:Introducing Relativity 5572:Einstein for Beginners 5475:Einstein and Eddington 5266:Einstein–Cartan theory 4999:Quantum neural network 2909:The Old Quantum Theory 2615:New Journal of Physics 2463:10.1098/rspa.1928.0121 2217:10.1103/PhysRev.30.705 2168:10.1103/physrev.30.705 1654: 1626:Which slit experiments 1614: 1553: 1546: 1526: 1501: 1474: 1400: 1342: 1330:Double-slit experiment 102: 5765:Einstein refrigerator 5755:Einstein's Blackboard 5634:(second wife; cousin) 5565:Einstein and Religion 5514:Albert Einstein Medal 5509:Albert Einstein Award 5367:The World as I See It 5306:Wave–particle duality 5286:Bohr–Einstein debates 5246:Cosmological constant 5226:Equivalence principle 5216:Einstein coefficients 5024:Quantum teleportation 4552:Wave–particle duality 4315:Wave–particle duality 4305:Relativistic particle 3442:Electron antineutrino 2838:on September 21, 2020 2792:(November 6, 2001) . 2339:10.1073/pnas.14.8.619 2269:10.1073/pnas.14.4.317 1713:Uncertainty principle 1652: 1612: 1582:series of experiments 1547: 1527: 1502: 1486: 1475: 1398: 1340: 1314:probability amplitude 993:series of experiments 887:Wave-particle duality 296:Elitzur–Vaidman 286:Davisson–Germer 103: 5644:Hans Albert Einstein 5593:I Am Albert Einstein 5539:Einstein Prize (APS) 5211:Photoelectric effect 5184:Theory of relativity 5055:Quantum field theory 4984:Quantum metamaterial 4929:Quantum cryptography 4659:Consistent histories 3545:Faddeev–Popov ghosts 3295:Particles in physics 1835:Planck, Max (1901). 1821:Traité de la lumiere 1818:Christiaan Huygens, 1536: 1532:emerges at an angle 1511: 1491: 1473:{\displaystyle E=hf} 1455: 1405:Photoelectric effect 1107:Schrödinger equation 1098:George Paget Thomson 1072:Schrödinger equation 1068:undulatory mechanics 1059:a few years before. 981:photoelectric effect 973:electromagnetic wave 953:black-body radiation 943:'s detection of the 561:Quantum field theory 473:Consistent histories 110:Schrödinger equation 37: 5296:Thought experiments 5040:Quantum fluctuation 5009:Quantum programming 4969:Quantum logic gates 4954:Quantum information 4934:Quantum electronics 4409:Classical mechanics 4320:Particle chauvinism 4263:Subatomic particles 2995:10.1038/nature09366 2987:2010Natur.467..301V 2883:1905AnP...322..132E 2702:2014NatPh..10..271A 2637:2013NJPh...15c3018B 2561:1928AnP...392...55B 2454:1928RSPSA.119..663R 2397:1927Natur.119Q.890T 2330:1928PNAS...14..619D 2260:1928PNAS...14..317D 2208:1927PhRv...30..705D 2159:1927PhRv...30..705D 2112:1927Natur.119..558D 2016:1926PhRv...28.1049S 1782:Leighton, Robert B. 1778:Feynman, Richard P. 1568:value which is the 1271:Curved arc shows a 1161:classical mechanics 1136:, and they display 1043:) that move with a 349:Stern–Gerlach 146:Classical mechanics 5745:Things named after 5607:Subtle is the Lord 5430:(1994 documentary) 5422:(1923 documentary) 5414:(1922 documentary) 5311:Gravitational wave 5194:General relativity 5189:Special relativity 5093:in popular culture 4875:Quantum algorithms 4723:Von Neumann–Wigner 4703:Objective collapse 4414:Old quantum theory 2870:Annalen der Physik 2549:Annalen der Physik 2543:Bethe, H. (1928). 1931:"XL. Cathode Rays" 1841:Annalen der Physik 1655: 1615: 1554: 1542: 1522: 1497: 1470: 1409:Compton scattering 1401: 1343: 929:Christiaan Huygens 889:is the concept in 537:Von Neumann–Wigner 517:Objective-collapse 316:Mach–Zehnder 306:Leggett inequality 301:Franck–Hertz 151:Old quantum theory 98: 5813: 5812: 5715:Awards and honors 5698:Siegbert Einstein 5586:Einstein's Cosmos 5136: 5135: 5110:Quantum mysticism 5088:Schrödinger's cat 5019:Quantum simulator 4989:Quantum metrology 4917:Quantum computing 4880:Quantum amplifier 4857:Quantum spacetime 4822:Quantum cosmology 4812:Quantum chemistry 4527:Scattering theory 4475:Zero-point energy 4470:Degenerate levels 4378:Quantum mechanics 4344: 4343: 4300:Massless particle 4108: 4107: 4104: 4103: 4069: 4068: 3932: 3931: 3744: 3743: 3740: 3739: 3692:Magnetic monopole 3640: 3639: 3531: 3530: 3472: 3471: 3452:Muon antineutrino 3437:Electron neutrino 3172:10.1119/1.1450558 3060:10.1063/5.0093411 2981:(7313): 301–304. 2942:(11): 8185–8189. 2936:Physical Review A 2811:10.1063/1.1480788 2710:10.1038/nphys2863 2106:(2998): 558–560. 2063:10.1063/1.3001830 1915:978-0-486-26126-3 1881:978-0-691-10250-4 1805:978-0-201-02118-9 1791:Quantum Mechanics 1786:Sands, Matthew L. 1748:Quantum Mechanics 1610: 1227:Wave interference 1171:characterized by 1163:; they have some 1138:wave interference 1070:, now called the 1064:Erwin Schrödinger 901:concepts such as 891:quantum mechanics 884: 883: 591:Scattering theory 571:Quantum computing 344:Schrödinger's cat 276:Bell's inequality 84: 59: 28:Quantum mechanics 5848: 5801: 5800: 5700:(distant cousin) 5694:(great-grandson) 5656:Hermann Einstein 5638:Lieserl Einstein 5316:Tea leaf paradox 5163: 5156: 5149: 5140: 5139: 5126: 5125: 4837:Quantum geometry 4832:Quantum dynamics 4689:Superdeterminism 4585:Matrix mechanics 4440:Bra–ket notation 4371: 4364: 4357: 4348: 4347: 4334: 4310:Virtual particle 4081:Mesonic molecule 4015: 4014: 4011: 4010: 3856:Bottom eta meson 3764: 3763: 3755: 3754: 3727:W′ and Z′ bosons 3717:Sterile neutrino 3702:Majorana fermion 3569: 3568: 3560: 3559: 3483: 3482: 3462:Tau antineutrino 3317: 3316: 3308: 3307: 3288: 3281: 3274: 3265: 3264: 3260: 3258: 3256: 3237: 3235: 3233: 3214: 3212: 3210: 3184: 3183: 3157: 3148: 3137: 3136: 3110: 3086: 3080: 3079: 3053: 3029: 3023: 3022: 2966: 2960: 2959: 2927: 2921: 2919: 2918:on 11 June 2009. 2917: 2911:. Archived from 2906: 2897: 2895: 2885: 2862:Einstein, Albert 2858: 2852: 2847: 2845: 2843: 2834:. Archived from 2833: 2813: 2790:Hawking, Stephen 2786: 2780: 2779: 2768:10.2307/27757381 2751: 2745: 2744: 2736: 2730: 2729: 2695: 2671: 2665: 2664: 2630: 2606: 2597: 2596: 2594: 2593: 2579: 2573: 2572: 2540: 2531: 2530: 2490: 2484: 2483: 2465: 2448:(783): 663–667. 2433: 2427: 2426: 2408: 2406:10.1038/119890a0 2376: 2370: 2369: 2359: 2341: 2309: 2300: 2299: 2289: 2271: 2239: 2230: 2229: 2219: 2187: 2181: 2180: 2170: 2138: 2132: 2131: 2120:10.1038/119558a0 2097: 2081: 2075: 2074: 2042: 2036: 2035: 2010:(6): 1049–1070. 1995: 1989: 1988: 1986: 1984: 1974: 1965: 1959: 1958: 1941:(269): 293–316. 1926: 1920: 1919: 1901: 1886: 1885: 1865: 1859: 1858: 1856: 1832: 1826: 1816: 1810: 1809: 1774: 1763: 1762: 1742: 1709: 1684: 1635:). Many similar 1619:angular momentum 1611: 1551: 1549: 1548: 1543: 1531: 1529: 1528: 1523: 1521: 1506: 1504: 1503: 1498: 1479: 1477: 1476: 1471: 1448:of the light by 1372: 1361: 1275:trajectory of a 1268: 1256: 1238: 1223: 1083:Clinton Davisson 1024:Louis de Broglie 979:interpreted the 876: 869: 862: 503:Superdeterminism 156:Bra–ket notation 107: 105: 104: 99: 91: 86: 85: 77: 65: 60: 58: 47: 19: 18: 5856: 5855: 5851: 5850: 5849: 5847: 5846: 5845: 5816: 5815: 5814: 5809: 5789: 5740:Religious views 5735:Political views 5703: 5688:(granddaughter) 5686:Evelyn Einstein 5674:Robert Einstein 5668:Eduard Einstein 5612: 5549: 5543: 5497: 5467:Einstein's Gift 5401: 5394: 5335:Annus mirabilis 5320: 5291:Teleparallelism 5236:Einstein radius 5206:Brownian motion 5172: 5170:Albert Einstein 5167: 5137: 5132: 5114: 5100:Wigner's friend 5076: 5067:Quantum gravity 5028: 5014:Quantum sensing 4994:Quantum network 4974:Quantum machine 4944:Quantum imaging 4907:Quantum circuit 4902:Quantum channel 4861: 4807:Quantum biology 4793: 4769:Elitzur–Vaidman 4744:Davisson–Germer 4727: 4679:Hidden-variable 4669:de Broglie–Bohm 4646:Interpretations 4640: 4604: 4558: 4445:Complementarity 4423: 4380: 4375: 4345: 4340: 4324: 4278:Nuclear physics 4227: 4191: 4127:Davydov soliton 4100: 4065: 4039: 4000: 3928: 3900: 3827: 3736: 3636: 3595: 3549: 3527: 3509: 3468: 3388: 3297: 3292: 3254: 3252: 3231: 3229: 3217: 3208: 3206: 3193: 3188: 3187: 3155: 3149: 3140: 3087: 3083: 3030: 3026: 2967: 2963: 2928: 2924: 2915: 2904: 2859: 2855: 2841: 2839: 2822: 2787: 2783: 2752: 2748: 2737: 2733: 2672: 2668: 2607: 2600: 2591: 2589: 2581: 2580: 2576: 2541: 2534: 2491: 2487: 2434: 2430: 2377: 2373: 2310: 2303: 2240: 2233: 2196:Physical Review 2188: 2184: 2147:Physical Review 2139: 2135: 2095: 2083: 2082: 2078: 2043: 2039: 2004:Physical Review 1996: 1992: 1982: 1980: 1972: 1966: 1962: 1927: 1923: 1916: 1902: 1889: 1882: 1866: 1862: 1833: 1829: 1817: 1813: 1806: 1775: 1766: 1759: 1743: 1736: 1731: 1707: 1682: 1675: 1628: 1603: 1601: 1562:Planck constant 1537: 1534: 1533: 1514: 1512: 1509: 1508: 1492: 1489: 1488: 1456: 1453: 1452: 1431:Albert Einstein 1411: 1403:Main articles: 1393: 1384: 1383: 1382: 1381: 1380: 1373: 1364: 1363: 1362: 1332: 1326: 1310:magnetic moment 1306:electric charge 1291: 1290: 1289: 1288: 1282: 1281: 1280: 1269: 1261: 1260: 1257: 1248: 1247: 1246: 1239: 1231: 1230: 1224: 1215: 1214: 1125: 1105:based upon the 1057:Albert Einstein 1016:Robert Millikan 1008: 1002: 921: 916: 880: 851: 850: 849: 614: 606: 605: 551: 550:Advanced topics 543: 542: 541: 493:Hidden-variable 483:de Broglie–Bohm 462: 460:Interpretations 452: 451: 450: 420: 412: 411: 410: 368: 360: 359: 358: 325: 281:CHSH inequality 270: 262: 261: 260: 189:Complementarity 183: 175: 174: 173: 141: 112: 87: 76: 75: 61: 51: 46: 38: 35: 34: 17: 12: 11: 5: 5854: 5844: 5843: 5838: 5833: 5828: 5811: 5810: 5808: 5807: 5794: 5791: 5790: 5788: 5787: 5782: 5777: 5772: 5767: 5762: 5757: 5752: 5747: 5742: 5737: 5732: 5727: 5722: 5717: 5711: 5709: 5705: 5704: 5702: 5701: 5695: 5689: 5683: 5677: 5671: 5665: 5659: 5653: 5647: 5641: 5635: 5629: 5622: 5620: 5614: 5613: 5611: 5610: 5603: 5596: 5589: 5582: 5575: 5568: 5561: 5553: 5551: 5545: 5544: 5542: 5541: 5536: 5531: 5526: 5521: 5516: 5511: 5505: 5503: 5499: 5498: 5496: 5495: 5487: 5479: 5478:(2008 TV film) 5471: 5463: 5455: 5447: 5443:Young Einstein 5439: 5435:Insignificance 5431: 5423: 5415: 5406: 5404: 5396: 5395: 5393: 5392: 5386: 5383:Why Socialism? 5379: 5371: 5363: 5355: 5347: 5340: 5330: 5328: 5322: 5321: 5319: 5318: 5313: 5308: 5303: 5298: 5293: 5288: 5283: 5278: 5273: 5268: 5263: 5258: 5253: 5248: 5243: 5238: 5233: 5228: 5223: 5221:Einstein solid 5218: 5213: 5208: 5203: 5198: 5197: 5196: 5191: 5180: 5178: 5174: 5173: 5166: 5165: 5158: 5151: 5143: 5134: 5133: 5131: 5130: 5119: 5116: 5115: 5113: 5112: 5107: 5102: 5097: 5096: 5095: 5084: 5082: 5078: 5077: 5075: 5074: 5069: 5064: 5063: 5062: 5052: 5047: 5045:Casimir effect 5042: 5036: 5034: 5030: 5029: 5027: 5026: 5021: 5016: 5011: 5006: 5004:Quantum optics 5001: 4996: 4991: 4986: 4981: 4976: 4971: 4966: 4961: 4956: 4951: 4946: 4941: 4936: 4931: 4926: 4925: 4924: 4914: 4909: 4904: 4899: 4898: 4897: 4887: 4882: 4877: 4871: 4869: 4863: 4862: 4860: 4859: 4854: 4849: 4844: 4839: 4834: 4829: 4824: 4819: 4814: 4809: 4803: 4801: 4795: 4794: 4792: 4791: 4786: 4781: 4779:Quantum eraser 4776: 4771: 4766: 4761: 4756: 4751: 4746: 4741: 4735: 4733: 4729: 4728: 4726: 4725: 4720: 4715: 4710: 4705: 4700: 4695: 4694: 4693: 4692: 4691: 4676: 4671: 4666: 4661: 4656: 4650: 4648: 4642: 4641: 4639: 4638: 4633: 4628: 4623: 4618: 4612: 4610: 4606: 4605: 4603: 4602: 4597: 4592: 4587: 4582: 4577: 4572: 4566: 4564: 4560: 4559: 4557: 4556: 4555: 4554: 4549: 4539: 4534: 4529: 4524: 4519: 4514: 4509: 4504: 4499: 4494: 4489: 4484: 4479: 4478: 4477: 4472: 4467: 4462: 4452: 4450:Density matrix 4447: 4442: 4437: 4431: 4429: 4425: 4424: 4422: 4421: 4416: 4411: 4406: 4405: 4404: 4394: 4388: 4386: 4382: 4381: 4374: 4373: 4366: 4359: 4351: 4342: 4341: 4337:Physics portal 4329: 4326: 4325: 4323: 4322: 4317: 4312: 4307: 4302: 4297: 4292: 4291: 4290: 4280: 4275: 4270: 4265: 4260: 4259: 4258: 4251:Standard Model 4248: 4247: 4246: 4235: 4233: 4229: 4228: 4226: 4225: 4220: 4218:Quasiparticles 4215: 4210: 4205: 4199: 4197: 4193: 4192: 4190: 4189: 4184: 4179: 4174: 4169: 4164: 4159: 4154: 4149: 4144: 4139: 4134: 4129: 4124: 4118: 4116: 4114:Quasiparticles 4110: 4109: 4106: 4105: 4102: 4101: 4099: 4098: 4093: 4088: 4083: 4077: 4075: 4071: 4070: 4067: 4066: 4064: 4063: 4058: 4053: 4047: 4045: 4041: 4040: 4038: 4037: 4032: 4027: 4021: 4019: 4008: 4002: 4001: 3999: 3998: 3993: 3988: 3987: 3986: 3981: 3976: 3971: 3966: 3961: 3951: 3946: 3940: 3938: 3934: 3933: 3930: 3929: 3927: 3926: 3921: 3910: 3908: 3906:Exotic hadrons 3902: 3901: 3899: 3898: 3893: 3888: 3883: 3878: 3873: 3868: 3863: 3858: 3853: 3848: 3843: 3837: 3835: 3829: 3828: 3826: 3825: 3820: 3815: 3810: 3805: 3800: 3799: 3798: 3793: 3788: 3783: 3772: 3770: 3761: 3752: 3746: 3745: 3742: 3741: 3738: 3737: 3735: 3734: 3732:X and Y bosons 3729: 3724: 3719: 3714: 3709: 3704: 3699: 3694: 3689: 3684: 3679: 3674: 3669: 3664: 3659: 3654: 3648: 3646: 3642: 3641: 3638: 3637: 3635: 3634: 3624: 3619: 3614: 3609: 3603: 3601: 3597: 3596: 3594: 3593: 3588: 3583: 3577: 3575: 3566: 3557: 3551: 3550: 3548: 3547: 3541: 3539: 3533: 3532: 3529: 3528: 3526: 3525: 3519: 3517: 3511: 3510: 3508: 3507: 3505:W and Z bosons 3502: 3497: 3491: 3489: 3480: 3474: 3473: 3470: 3469: 3467: 3466: 3465: 3464: 3459: 3454: 3449: 3444: 3439: 3429: 3424: 3419: 3414: 3409: 3404: 3398: 3396: 3390: 3389: 3387: 3386: 3381: 3376: 3371: 3366: 3361: 3359:Strange (quark 3356: 3351: 3346: 3341: 3336: 3331: 3325: 3323: 3314: 3305: 3299: 3298: 3291: 3290: 3283: 3276: 3268: 3262: 3261: 3238: 3215: 3192: 3191:External links 3189: 3186: 3185: 3166:(3): 266–271. 3138: 3081: 3024: 2961: 2922: 2853: 2821:978-0553802023 2820: 2781: 2746: 2731: 2686:(4): 271–277. 2680:Nature Physics 2666: 2598: 2587:NobelPrize.org 2574: 2555:(17): 55–129. 2532: 2505:(2): 245–275. 2485: 2428: 2371: 2324:(8): 619–627. 2301: 2254:(4): 317–322. 2231: 2202:(6): 705–740. 2182: 2153:(6): 705–740. 2133: 2076: 2037: 1990: 1960: 1921: 1914: 1887: 1880: 1860: 1847:(3): 553–563. 1827: 1811: 1804: 1764: 1757: 1733: 1732: 1730: 1727: 1726: 1725: 1720: 1715: 1710: 1701: 1696: 1691: 1685: 1674: 1671: 1627: 1624: 1600: 1597: 1578:Arthur Compton 1541: 1520: 1517: 1496: 1481: 1480: 1469: 1466: 1463: 1460: 1423:Philipp Lenard 1415:Heinrich Hertz 1392: 1389: 1374: 1367: 1366: 1365: 1356: 1355: 1354: 1353: 1352: 1325: 1322: 1318:quasiparticles 1284: 1283: 1270: 1263: 1262: 1258: 1251: 1250: 1249: 1240: 1233: 1232: 1225: 1218: 1217: 1216: 1212: 1211: 1210: 1209: 1165:center of mass 1124: 1121: 1049:effective mass 1045:group velocity 1020:Charles Wilson 1004:Main article: 1001: 998: 989:Arthur Compton 941:François Arago 920: 917: 915: 912: 882: 881: 879: 878: 871: 864: 856: 853: 852: 848: 847: 842: 837: 832: 827: 822: 817: 812: 807: 802: 797: 792: 787: 782: 777: 772: 767: 762: 757: 752: 747: 742: 737: 732: 727: 722: 717: 712: 707: 702: 697: 692: 687: 682: 677: 672: 667: 662: 657: 652: 647: 642: 637: 632: 627: 622: 616: 615: 612: 611: 608: 607: 604: 603: 598: 593: 588: 586:Density matrix 583: 578: 573: 568: 563: 558: 552: 549: 548: 545: 544: 540: 539: 534: 529: 524: 519: 514: 509: 508: 507: 506: 505: 490: 485: 480: 475: 470: 464: 463: 458: 457: 454: 453: 449: 448: 443: 438: 433: 428: 422: 421: 418: 417: 414: 413: 409: 408: 403: 398: 393: 388: 383: 377: 376: 375: 369: 366: 365: 362: 361: 357: 356: 351: 346: 340: 339: 338: 337: 336: 334:Delayed-choice 329:Quantum eraser 324: 323: 318: 313: 308: 303: 298: 293: 288: 283: 278: 272: 271: 268: 267: 264: 263: 259: 258: 257: 256: 246: 241: 236: 231: 226: 221: 219:Quantum number 216: 211: 206: 201: 196: 191: 185: 184: 181: 180: 177: 176: 172: 171: 166: 160: 159: 158: 153: 148: 142: 139: 138: 135: 134: 133: 132: 127: 122: 114: 113: 108: 97: 94: 90: 83: 80: 74: 71: 68: 64: 57: 54: 50: 45: 42: 31: 30: 24: 23: 15: 9: 6: 4: 3: 2: 5853: 5842: 5839: 5837: 5834: 5832: 5829: 5827: 5824: 5823: 5821: 5806: 5805: 5796: 5795: 5792: 5786: 5783: 5781: 5778: 5776: 5773: 5771: 5768: 5766: 5763: 5761: 5758: 5756: 5753: 5751: 5748: 5746: 5743: 5741: 5738: 5736: 5733: 5731: 5728: 5726: 5723: 5721: 5718: 5716: 5713: 5712: 5710: 5706: 5699: 5696: 5693: 5690: 5687: 5684: 5681: 5678: 5675: 5672: 5669: 5666: 5663: 5662:Maja Einstein 5660: 5657: 5654: 5651: 5648: 5645: 5642: 5639: 5636: 5633: 5632:Elsa Einstein 5630: 5627: 5624: 5623: 5621: 5619: 5615: 5609: 5608: 5604: 5602: 5601: 5597: 5595: 5594: 5590: 5588: 5587: 5583: 5581: 5580: 5576: 5574: 5573: 5569: 5567: 5566: 5562: 5560: 5559: 5555: 5554: 5552: 5546: 5540: 5537: 5535: 5532: 5530: 5527: 5525: 5522: 5520: 5519:Kalinga Prize 5517: 5515: 5512: 5510: 5507: 5506: 5504: 5500: 5493: 5492: 5488: 5486:(2017 series) 5485: 5484: 5480: 5477: 5476: 5472: 5469: 5468: 5464: 5461: 5460: 5456: 5453: 5452: 5448: 5445: 5444: 5440: 5437: 5436: 5432: 5429: 5428: 5424: 5421: 5420: 5416: 5413: 5412: 5408: 5407: 5405: 5403: 5397: 5390: 5387: 5384: 5380: 5377: 5376: 5372: 5369: 5368: 5364: 5361: 5360: 5356: 5353: 5352: 5348: 5345: 5341: 5338: 5336: 5332: 5331: 5329: 5327: 5323: 5317: 5314: 5312: 5309: 5307: 5304: 5302: 5299: 5297: 5294: 5292: 5289: 5287: 5284: 5282: 5279: 5277: 5274: 5272: 5269: 5267: 5264: 5262: 5259: 5257: 5254: 5252: 5249: 5247: 5244: 5242: 5239: 5237: 5234: 5232: 5229: 5227: 5224: 5222: 5219: 5217: 5214: 5212: 5209: 5207: 5204: 5202: 5199: 5195: 5192: 5190: 5187: 5186: 5185: 5182: 5181: 5179: 5175: 5171: 5164: 5159: 5157: 5152: 5150: 5145: 5144: 5141: 5129: 5121: 5120: 5117: 5111: 5108: 5106: 5103: 5101: 5098: 5094: 5091: 5090: 5089: 5086: 5085: 5083: 5079: 5073: 5070: 5068: 5065: 5061: 5058: 5057: 5056: 5053: 5051: 5048: 5046: 5043: 5041: 5038: 5037: 5035: 5031: 5025: 5022: 5020: 5017: 5015: 5012: 5010: 5007: 5005: 5002: 5000: 4997: 4995: 4992: 4990: 4987: 4985: 4982: 4980: 4977: 4975: 4972: 4970: 4967: 4965: 4964:Quantum logic 4962: 4960: 4957: 4955: 4952: 4950: 4947: 4945: 4942: 4940: 4937: 4935: 4932: 4930: 4927: 4923: 4920: 4919: 4918: 4915: 4913: 4910: 4908: 4905: 4903: 4900: 4896: 4893: 4892: 4891: 4888: 4886: 4883: 4881: 4878: 4876: 4873: 4872: 4870: 4868: 4864: 4858: 4855: 4853: 4850: 4848: 4845: 4843: 4840: 4838: 4835: 4833: 4830: 4828: 4825: 4823: 4820: 4818: 4817:Quantum chaos 4815: 4813: 4810: 4808: 4805: 4804: 4802: 4800: 4796: 4790: 4787: 4785: 4784:Stern–Gerlach 4782: 4780: 4777: 4775: 4772: 4770: 4767: 4765: 4762: 4760: 4757: 4755: 4752: 4750: 4747: 4745: 4742: 4740: 4737: 4736: 4734: 4730: 4724: 4721: 4719: 4718:Transactional 4716: 4714: 4711: 4709: 4708:Quantum logic 4706: 4704: 4701: 4699: 4696: 4690: 4687: 4686: 4685: 4682: 4681: 4680: 4677: 4675: 4672: 4670: 4667: 4665: 4662: 4660: 4657: 4655: 4652: 4651: 4649: 4647: 4643: 4637: 4634: 4632: 4629: 4627: 4624: 4622: 4619: 4617: 4614: 4613: 4611: 4607: 4601: 4598: 4596: 4593: 4591: 4588: 4586: 4583: 4581: 4578: 4576: 4573: 4571: 4568: 4567: 4565: 4561: 4553: 4550: 4548: 4545: 4544: 4543: 4542:Wave function 4540: 4538: 4535: 4533: 4530: 4528: 4525: 4523: 4520: 4518: 4517:Superposition 4515: 4513: 4512:Quantum state 4510: 4508: 4505: 4503: 4500: 4498: 4495: 4493: 4490: 4488: 4485: 4483: 4480: 4476: 4473: 4471: 4468: 4466: 4465:Excited state 4463: 4461: 4458: 4457: 4456: 4453: 4451: 4448: 4446: 4443: 4441: 4438: 4436: 4433: 4432: 4430: 4426: 4420: 4417: 4415: 4412: 4410: 4407: 4403: 4400: 4399: 4398: 4395: 4393: 4390: 4389: 4387: 4383: 4379: 4372: 4367: 4365: 4360: 4358: 4353: 4352: 4349: 4339: 4338: 4333: 4327: 4321: 4318: 4316: 4313: 4311: 4308: 4306: 4303: 4301: 4298: 4296: 4295:Exotic matter 4293: 4289: 4286: 4285: 4284: 4283:Eightfold way 4281: 4279: 4276: 4274: 4273:Antiparticles 4271: 4269: 4266: 4264: 4261: 4257: 4254: 4253: 4252: 4249: 4245: 4242: 4241: 4240: 4237: 4236: 4234: 4230: 4224: 4221: 4219: 4216: 4214: 4211: 4209: 4206: 4204: 4201: 4200: 4198: 4194: 4188: 4185: 4183: 4180: 4178: 4175: 4173: 4170: 4168: 4165: 4163: 4160: 4158: 4155: 4153: 4150: 4148: 4145: 4143: 4140: 4138: 4135: 4133: 4130: 4128: 4125: 4123: 4120: 4119: 4117: 4115: 4111: 4097: 4094: 4092: 4089: 4087: 4084: 4082: 4079: 4078: 4076: 4072: 4062: 4059: 4057: 4054: 4052: 4049: 4048: 4046: 4042: 4036: 4033: 4031: 4028: 4026: 4023: 4022: 4020: 4016: 4012: 4009: 4007: 4003: 3997: 3994: 3992: 3989: 3985: 3982: 3980: 3977: 3975: 3972: 3970: 3967: 3965: 3962: 3960: 3957: 3956: 3955: 3952: 3950: 3947: 3945: 3944:Atomic nuclei 3942: 3941: 3939: 3935: 3925: 3922: 3919: 3915: 3912: 3911: 3909: 3907: 3903: 3897: 3894: 3892: 3889: 3887: 3884: 3882: 3879: 3877: 3876:Upsilon meson 3874: 3872: 3869: 3867: 3864: 3862: 3859: 3857: 3854: 3852: 3849: 3847: 3844: 3842: 3839: 3838: 3836: 3834: 3830: 3824: 3821: 3819: 3816: 3814: 3811: 3809: 3808:Lambda baryon 3806: 3804: 3801: 3797: 3794: 3792: 3789: 3787: 3784: 3782: 3779: 3778: 3777: 3774: 3773: 3771: 3769: 3765: 3762: 3760: 3756: 3753: 3751: 3747: 3733: 3730: 3728: 3725: 3723: 3720: 3718: 3715: 3713: 3710: 3708: 3705: 3703: 3700: 3698: 3695: 3693: 3690: 3688: 3685: 3683: 3680: 3678: 3675: 3673: 3670: 3668: 3667:Dual graviton 3665: 3663: 3660: 3658: 3655: 3653: 3650: 3649: 3647: 3643: 3632: 3628: 3625: 3623: 3620: 3618: 3615: 3613: 3610: 3608: 3605: 3604: 3602: 3598: 3592: 3589: 3587: 3584: 3582: 3579: 3578: 3576: 3574: 3570: 3567: 3565: 3564:Superpartners 3561: 3558: 3556: 3552: 3546: 3543: 3542: 3540: 3538: 3534: 3524: 3521: 3520: 3518: 3516: 3512: 3506: 3503: 3501: 3498: 3496: 3493: 3492: 3490: 3488: 3484: 3481: 3479: 3475: 3463: 3460: 3458: 3455: 3453: 3450: 3448: 3447:Muon neutrino 3445: 3443: 3440: 3438: 3435: 3434: 3433: 3430: 3428: 3425: 3423: 3420: 3418: 3415: 3413: 3410: 3408: 3405: 3403: 3400: 3399: 3397: 3395: 3391: 3385: 3382: 3380: 3379:Bottom (quark 3377: 3375: 3372: 3370: 3367: 3365: 3362: 3360: 3357: 3355: 3352: 3350: 3347: 3345: 3342: 3340: 3337: 3335: 3332: 3330: 3327: 3326: 3324: 3322: 3318: 3315: 3313: 3309: 3306: 3304: 3300: 3296: 3289: 3284: 3282: 3277: 3275: 3270: 3269: 3266: 3251: 3247: 3243: 3239: 3228: 3224: 3220: 3216: 3204: 3200: 3195: 3194: 3181: 3177: 3173: 3169: 3165: 3161: 3154: 3147: 3145: 3143: 3134: 3130: 3126: 3122: 3118: 3114: 3109: 3104: 3101:(1): 015005. 3100: 3096: 3092: 3085: 3077: 3073: 3069: 3065: 3061: 3057: 3052: 3047: 3043: 3039: 3035: 3028: 3020: 3016: 3012: 3008: 3004: 3000: 2996: 2992: 2988: 2984: 2980: 2976: 2972: 2965: 2957: 2953: 2949: 2945: 2941: 2937: 2933: 2926: 2914: 2910: 2903: 2900:Einstein, A. 2894: 2889: 2884: 2879: 2876:(6): 132–48. 2875: 2871: 2867: 2863: 2857: 2850: 2837: 2832: 2827: 2823: 2817: 2812: 2807: 2803: 2799: 2798:Physics Today 2795: 2791: 2785: 2777: 2773: 2769: 2765: 2761: 2757: 2750: 2742: 2735: 2727: 2723: 2719: 2715: 2711: 2707: 2703: 2699: 2694: 2689: 2685: 2681: 2677: 2670: 2662: 2658: 2654: 2650: 2646: 2642: 2638: 2634: 2629: 2624: 2620: 2616: 2612: 2605: 2603: 2588: 2584: 2578: 2570: 2566: 2562: 2558: 2554: 2551:(in German). 2550: 2546: 2539: 2537: 2528: 2524: 2520: 2516: 2512: 2508: 2504: 2500: 2496: 2489: 2481: 2477: 2473: 2469: 2464: 2459: 2455: 2451: 2447: 2443: 2439: 2432: 2424: 2420: 2416: 2412: 2407: 2402: 2398: 2394: 2391:(3007): 890. 2390: 2386: 2382: 2375: 2367: 2363: 2358: 2353: 2349: 2345: 2340: 2335: 2331: 2327: 2323: 2319: 2315: 2308: 2306: 2297: 2293: 2288: 2283: 2279: 2275: 2270: 2265: 2261: 2257: 2253: 2249: 2245: 2238: 2236: 2227: 2223: 2218: 2213: 2209: 2205: 2201: 2197: 2193: 2186: 2178: 2174: 2169: 2164: 2160: 2156: 2152: 2148: 2144: 2137: 2129: 2125: 2121: 2117: 2113: 2109: 2105: 2101: 2094: 2090: 2086: 2080: 2072: 2068: 2064: 2060: 2056: 2052: 2051:Physics Today 2048: 2041: 2033: 2029: 2025: 2021: 2017: 2013: 2009: 2005: 2001: 1994: 1978: 1971: 1964: 1956: 1952: 1948: 1944: 1940: 1936: 1932: 1925: 1917: 1911: 1907: 1900: 1898: 1896: 1894: 1892: 1883: 1877: 1873: 1872: 1864: 1855: 1850: 1846: 1843:(in German). 1842: 1838: 1831: 1824: 1822: 1815: 1807: 1801: 1797: 1793: 1792: 1787: 1783: 1779: 1773: 1771: 1769: 1760: 1754: 1750: 1749: 1741: 1739: 1734: 1724: 1721: 1719: 1716: 1714: 1711: 1705: 1702: 1700: 1697: 1695: 1692: 1689: 1686: 1680: 1677: 1676: 1670: 1666: 1662: 1660: 1659:phase shifter 1651: 1647: 1645: 1640: 1638: 1634: 1623: 1620: 1596: 1594: 1593:laser cooling 1590: 1585: 1583: 1579: 1575: 1571: 1570:work function 1567: 1563: 1559: 1539: 1518: 1515: 1494: 1485: 1467: 1464: 1461: 1458: 1451: 1450: 1449: 1447: 1444: 1440: 1437: 1432: 1428: 1424: 1420: 1416: 1410: 1406: 1397: 1388: 1379: 1371: 1360: 1351: 1347: 1339: 1335: 1331: 1321: 1319: 1315: 1311: 1307: 1303: 1299: 1294: 1287: 1278: 1274: 1273:cloud chamber 1267: 1255: 1244: 1237: 1228: 1222: 1208: 1206: 1202: 1198: 1194: 1190: 1186: 1182: 1178: 1174: 1170: 1166: 1162: 1157: 1155: 1151: 1147: 1146:seismic waves 1143: 1139: 1135: 1131: 1130:wave equation 1120: 1117: 1112: 1108: 1104: 1099: 1095: 1091: 1086: 1084: 1080: 1075: 1073: 1069: 1065: 1060: 1058: 1054: 1050: 1046: 1042: 1037: 1036:standing wave 1033: 1029: 1025: 1021: 1017: 1013: 1012:J. J. Thomson 1007: 997: 994: 990: 986: 982: 978: 974: 970: 966: 962: 958: 954: 950: 946: 942: 939:in 1801, and 938: 934: 930: 926: 911: 908: 904: 900: 896: 892: 888: 877: 872: 870: 865: 863: 858: 857: 855: 854: 846: 843: 841: 838: 836: 833: 831: 828: 826: 823: 821: 818: 816: 813: 811: 808: 806: 803: 801: 798: 796: 793: 791: 788: 786: 783: 781: 778: 776: 773: 771: 768: 766: 763: 761: 758: 756: 753: 751: 748: 746: 743: 741: 738: 736: 733: 731: 728: 726: 723: 721: 718: 716: 713: 711: 708: 706: 703: 701: 698: 696: 693: 691: 688: 686: 683: 681: 678: 676: 673: 671: 668: 666: 663: 661: 658: 656: 653: 651: 648: 646: 643: 641: 638: 636: 633: 631: 628: 626: 623: 621: 618: 617: 610: 609: 602: 599: 597: 594: 592: 589: 587: 584: 582: 579: 577: 576:Quantum chaos 574: 572: 569: 567: 564: 562: 559: 557: 554: 553: 547: 546: 538: 535: 533: 532:Transactional 530: 528: 525: 523: 522:Quantum logic 520: 518: 515: 513: 510: 504: 501: 500: 499: 496: 495: 494: 491: 489: 486: 484: 481: 479: 476: 474: 471: 469: 466: 465: 461: 456: 455: 447: 444: 442: 439: 437: 434: 432: 429: 427: 424: 423: 416: 415: 407: 404: 402: 399: 397: 394: 392: 389: 387: 384: 382: 379: 378: 374: 371: 370: 364: 363: 355: 352: 350: 347: 345: 342: 341: 335: 332: 331: 330: 327: 326: 322: 319: 317: 314: 312: 309: 307: 304: 302: 299: 297: 294: 292: 289: 287: 284: 282: 279: 277: 274: 273: 266: 265: 255: 252: 251: 250: 249:Wave function 247: 245: 242: 240: 237: 235: 232: 230: 229:Superposition 227: 225: 222: 220: 217: 215: 212: 210: 207: 205: 202: 200: 197: 195: 192: 190: 187: 186: 179: 178: 170: 167: 165: 162: 161: 157: 154: 152: 149: 147: 144: 143: 137: 136: 131: 128: 126: 123: 121: 118: 117: 116: 115: 111: 78: 72: 55: 52: 48: 40: 33: 32: 29: 26: 25: 21: 20: 5802: 5770:Einsteinhaus 5650:Pauline Koch 5628:(first wife) 5626:Mileva Marić 5605: 5598: 5591: 5584: 5577: 5570: 5563: 5556: 5489: 5481: 5473: 5465: 5457: 5449: 5441: 5433: 5425: 5417: 5409: 5373: 5365: 5357: 5349: 5334: 5305: 4847:Quantum mind 4759:Franck–Hertz 4621:Klein–Gordon 4570:Formulations 4563:Formulations 4551: 4492:Interference 4482:Entanglement 4460:Ground state 4455:Energy level 4428:Fundamentals 4392:Introduction 4335: 4314: 4006:Hypothetical 3954:Exotic atoms 3823:Omega baryon 3813:Sigma baryon 3803:Delta baryon 3555:Hypothetical 3537:Ghost fields 3523:Higgs boson 3457:Tau neutrino 3349:Charm (quark 3253:. Retrieved 3230:. Retrieved 3223:PhysicsQuest 3222: 3209:December 12, 3207:. Retrieved 3203:HyperPhysics 3202: 3163: 3159: 3098: 3094: 3084: 3041: 3037: 3027: 2978: 2974: 2964: 2939: 2935: 2925: 2913:the original 2908: 2873: 2869: 2856: 2842:December 14, 2840:. Retrieved 2836:the original 2801: 2797: 2784: 2759: 2755: 2749: 2740: 2734: 2683: 2679: 2669: 2618: 2614: 2590:. Retrieved 2586: 2577: 2552: 2548: 2502: 2498: 2488: 2445: 2441: 2431: 2388: 2384: 2374: 2321: 2317: 2251: 2247: 2199: 2195: 2185: 2150: 2146: 2136: 2103: 2099: 2089:L. H. Germer 2079: 2057:(1): 34–41. 2054: 2050: 2040: 2007: 2003: 1993: 1981:. Retrieved 1976: 1963: 1938: 1934: 1924: 1905: 1870: 1863: 1844: 1840: 1830: 1820: 1814: 1790: 1747: 1667: 1663: 1656: 1641: 1629: 1616: 1586: 1580:performed a 1565: 1557: 1555: 1445: 1438: 1419:cathode rays 1412: 1385: 1377: 1348: 1344: 1333: 1295: 1292: 1285: 1243:trajectories 1197:tennis balls 1169:trajectories 1158: 1156:, and more. 1126: 1087: 1076: 1067: 1061: 1047:and have an 1041:wave packets 1031: 1009: 991:performed a 968: 949:Planck's law 945:Poisson spot 933:Thomas Young 925:Isaac Newton 922: 886: 885: 431:Klein–Gordon 367:Formulations 204:Energy level 199:Entanglement 182:Fundamentals 169:Interference 120:Introduction 5826:Dichotomies 5775:Einsteinium 5548:Books about 5494:(2023 film) 5491:Oppenheimer 5470:(2003 play) 5462:(1994 film) 5454:(1993 play) 5446:(1988 film) 5438:(1985 film) 5281:EPR paradox 5105:EPR paradox 4885:Quantum bus 4754:Double-slit 4732:Experiments 4698:Many-worlds 4636:Schrödinger 4600:Phase space 4590:Schrödinger 4580:Interaction 4537:Uncertainty 4507:Nonlocality 4502:Measurement 4497:Decoherence 4487:Hamiltonian 4288:Quark model 4056:Theta meson 3959:Positronium 3871:Omega meson 3866:J/psi meson 3796:Antineutron 3707:Dark photon 3672:Graviphoton 3631:Stop squark 3339:Down (quark 3242:Mack, Katie 2762:: 299–322. 2693:1410.0270v1 2085:C. Davisson 1983:25 February 1718:Matter wave 1589:solar sails 1205:sand grains 1154:radio waves 1150:sound waves 1142:water waves 1134:diffraction 1111:Bragg's law 1006:Matter wave 820:von Neumann 805:Schrödinger 581:EPR paradox 512:Many-worlds 446:Schrödinger 401:Schrödinger 396:Phase-space 386:Interaction 291:Double-slit 269:Experiments 244:Uncertainty 214:Nonlocality 209:Measurement 194:Decoherence 164:Hamiltonian 5820:Categories 5780:Max Talmey 5682:(grandson) 5640:(daughter) 5400:In popular 5033:Extensions 4867:Technology 4713:Relational 4664:Copenhagen 4575:Heisenberg 4522:Tunnelling 4385:Background 4030:Heptaquark 3991:Superatoms 3924:Pentaquark 3914:Tetraquark 3896:Quarkonium 3786:Antiproton 3687:Leptoquark 3622:Neutralino 3384:antiquark) 3374:antiquark) 3369:Top (quark 3364:antiquark) 3354:antiquark) 3344:antiquark) 3334:antiquark) 3303:Elementary 3255:August 31, 3232:August 31, 3051:2203.00477 2592:2024-03-18 1758:0486409244 1729:References 1328:See also: 1241:Classical 1193:spacecraft 1177:velocities 1116:Otto Stern 1103:Hans Bethe 1096:surfaces. 1053:wavevector 975:. In 1905 961:oscillator 957:Max Planck 815:Sommerfeld 730:Heisenberg 725:Gutzwiller 665:de Broglie 613:Scientists 527:Relational 478:Copenhagen 381:Heisenberg 239:Tunnelling 140:Background 5841:Particles 4739:Bell test 4609:Equations 4435:Born rule 4268:Particles 4213:Particles 4172:Polariton 4162:Plasmaron 4132:Dropleton 4025:Hexaquark 3996:Molecules 3984:Protonium 3861:Phi meson 3846:Rho meson 3818:Xi baryon 3750:Composite 3586:Gravitino 3329:Up (quark 3197:R. Nave. 3180:0002-9505 3125:0034-6861 3108:1407.2930 3076:247187983 3068:0003-6951 3003:0028-0836 2831:120382028 2718:1745-2473 2653:1367-2630 2628:1210.6243 2527:171025814 2519:0007-0874 2472:0950-1207 2415:0028-0836 2348:0027-8424 2278:0027-8424 2226:0031-899X 2177:0031-899X 2071:0031-9228 2032:0031-899X 1955:1941-5982 1637:proposals 1633:coherence 1617:Normally 1566:threshold 1540:θ 1516:λ 1495:λ 1443:frequency 1427:intensity 1173:positions 1077:In 1926, 899:classical 845:Zeilinger 690:Ehrenfest 419:Equations 96:⟩ 93:Ψ 82:^ 70:⟩ 67:Ψ 44:ℏ 5804:Category 5730:Memorial 5676:(cousin) 5664:(sister) 5658:(father) 5652:(mother) 5550:Einstein 5385:" (1949) 5346:" (1905) 5128:Category 4922:Timeline 4674:Ensemble 4654:Bayesian 4547:Collapse 4419:Glossary 4402:Timeline 4244:timeline 4096:R-hadron 4051:Glueball 4035:Skyrmion 3969:Tauonium 3682:Inflaton 3677:Graviton 3657:Curvaton 3627:Sfermion 3617:Higgsino 3612:Chargino 3573:Gauginos 3432:Neutrino 3417:Antimuon 3407:Positron 3402:Electron 3312:Fermions 3133:34901303 3011:20844532 2864:(1905). 2776:27757381 2726:56438353 2480:98311959 2366:16587378 2296:16587341 2091:(1927). 1788:(2007). 1673:See also 1519:′ 1277:positron 1094:Ni metal 1079:Max Born 1028:electron 977:Einstein 903:particle 770:Millikan 695:Einstein 680:Davisson 635:Blackett 620:Aharonov 488:Ensemble 468:Bayesian 373:Overview 254:Collapse 234:Symmetry 125:Glossary 5708:Related 5402:culture 5177:Physics 5081:Related 5060:History 4799:Science 4631:Rydberg 4397:History 4232:Related 4203:Baryons 4177:Polaron 4167:Plasmon 4142:Fracton 4137:Exciton 4091:Diquark 4086:Pomeron 4061:T meson 4018:Baryons 3979:Pionium 3964:Muonium 3891:D meson 3886:B meson 3791:Neutron 3776:Nucleon 3768:Baryons 3759:Hadrons 3722:Tachyon 3697:Majoron 3662:Dilaton 3591:Photino 3427:Antitau 3394:Leptons 3019:2970408 2983:Bibcode 2956:9906912 2878:Bibcode 2849:Alt URL 2698:Bibcode 2633:Bibcode 2557:Bibcode 2450:Bibcode 2423:4122313 2393:Bibcode 2357:1085652 2326:Bibcode 2287:1085484 2256:Bibcode 2204:Bibcode 2155:Bibcode 2128:4104602 2108:Bibcode 2012:Bibcode 1560:is the 1201:bullets 1189:planets 914:History 895:quantum 810:Simmons 800:Rydberg 765:Moseley 745:Kramers 735:Hilbert 720:Glauber 715:Feynman 700:Everett 670:Compton 441:Rydberg 130:History 5618:Family 5502:Prizes 5483:Genius 5391:(1955) 5378:(1938) 5370:(1934) 5362:(1922) 5354:(1916) 5339:(1905) 5337:papers 4774:Popper 4208:Mesons 4157:Phonon 4152:Magnon 4074:Others 4044:Mesons 3937:Others 3833:Mesons 3781:Proton 3645:Others 3600:Others 3581:Gluino 3515:Scalar 3495:Photon 3478:Bosons 3321:Quarks 3178:  3131:  3123:  3074:  3066:  3017:  3009:  3001:  2975:Nature 2954:  2828:  2818:  2774:  2724:  2716:  2661:832961 2659:  2651:  2525:  2517:  2478:  2470:  2421:  2413:  2385:Nature 2364:  2354:  2346:  2294:  2284:  2276:  2224:  2175:  2126:  2100:Nature 2069:  2030:  1953:  1912:  1878:  1802:  1755:  1574:photon 1556:where 1436:energy 1298:quanta 1181:forces 1018:, and 985:photon 965:energy 840:Zeeman 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Index

Quantum mechanics
Schrödinger equation
Introduction
Glossary
History
Classical mechanics
Old quantum theory
Bra–ket notation
Hamiltonian
Interference
Complementarity
Decoherence
Entanglement
Energy level
Measurement
Nonlocality
Quantum number
State
Superposition
Symmetry
Tunnelling
Uncertainty
Wave function
Collapse
Bell's inequality
CHSH inequality
Davisson–Germer
Double-slit
Elitzur–Vaidman
Franck–Hertz

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