Editing Wave–particle duality (section)

== History ==

=== Wave-particle duality of light ===
In the late 17th century, Sir [[Isaac Newton]] had advocated that light was [[Corpuscular theory of light|corpuscular]] (particulate), but [[Christiaan Huygens]] took an opposing wave description. While Newton had favored a particle approach, he was the first to attempt to reconcile both wave and particle theories of light, and the only one in his time to consider both, thereby anticipating modern wave-particle duality.<ref>{{Cite book |last=Finkelstein |first=David Ritz |author-link=David Finkelstein |url=https://books.google.com/books?id=OvjsCAAAQBAJ&pg=PA156 |title=Quantum Relativity |date=1996 |publisher=Springer Berlin Heidelberg |isbn=978-3-642-64612-6 |location= |pages=156, 169–170 |language=en |doi=10.1007/978-3-642-60936-7}}</ref><ref>{{Cite book |last=Arianrhod |first=Robyn |author-link=Robyn Arianrhod |url=https://books.google.com/books?id=ODDwiGtK1RQC&pg=PA232 |title=Seduced by Logic: Émilie Du Châtelet, Mary Somerville and the Newtonian Revolution |date=2012 |publisher=Oxford University Press |isbn=978-0-19-993161-3 |location=New York |pages=232 |language=en}}</ref> [[Thomas Young (scientist)|Thomas Young]]'s [[Young's interference experiment|interference experiments]] in 1801, and [[François Arago]]'s detection of the [[Poisson spot]] in 1819, validated Huygens' wave models. However, the wave model was challenged in 1901 by [[Planck's law]] for [[black-body radiation]].<ref>{{Cite journal |last=Planck |first=Max |date=1901 |title=Ueber das Gesetz der Energieverteilung im Normalspectrum |journal=Annalen der Physik |language=de |volume=309 |issue=3 |pages=553–563 |doi=10.1002/andp.19013090310|doi-access=free }}</ref> [[Max Planck]] heuristically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged [[Oscillation|oscillator]] in a cavity that contained black-body radiation could only change its [[energy]] in a minimal increment, ''E'', that was proportional to the frequency of its associated [[electromagnetic wave]]. In 1905 [[Albert Einstein]] interpreted the [[photoelectric effect]] also with discrete energies for photons.<ref>{{Cite book |last=Einstein |first=Albert |title=The collected papers of Albert Einstein. 3: The Swiss years: writings, 1909 - 1911: [English translation] |date=1993 |publisher=Princeton Univ. Pr |isbn=978-0-691-10250-4 |location=Princeton, NJ}}</ref> These both indicate particle behavior. Despite confirmation by various experimental observations, the [[photon]] theory (as it came to be called) remained controversial until [[Arthur Compton]] performed a [[Compton effect|series of experiments]] from 1922 to 1924 demonstrating the momentum of light.<ref name="Whittaker2">{{Cite book |last=Whittaker |first=Edmund T. |title=A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 |date=1989 |publisher=Dover Publ |isbn=978-0-486-26126-3 |edition=Repr |location=New York}}</ref>{{rp|211}} The experimental evidence of particle-like momentum and energy seemingly contradicted the earlier work demonstrating wave-like interference of light.

=== Wave-particle duality of matter ===
{{Main|Matter wave}}
The contradictory evidence from electrons arrived in the opposite order. Many experiments by [[J. J. Thomson]],<ref name="Whittaker2" />{{rp|I:361}} [[Robert Millikan]],<ref name="Whittaker2" />{{rp|I:89}} and [[Charles Thomson Rees Wilson|Charles Wilson]]<ref name="Whittaker2" />{{rp|I:4}}  among others had shown that free electrons had particle properties, for instance, the measurement of their mass by Thomson in 1897.<ref>{{Cite journal |last=Thomson |first=J. J. |date=1897 |title=XL. Cathode Rays |url=https://www.tandfonline.com/doi/full/10.1080/14786449708621070 |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |language=en |volume=44 |issue=269 |pages=293–316 |doi=10.1080/14786449708621070 |issn=1941-5982|url-access=subscription }}</ref> In 1924, [[Louis de Broglie]] introduced his theory of [[electron]] waves in his PhD thesis ''Recherches sur la théorie des quanta''.<ref name="Broglie">{{cite web |last1=de Broglie |first1=Louis Victor |title=On the Theory of Quanta |url=https://fondationlouisdebroglie.org/LDB-oeuvres/De_Broglie_Kracklauer.pdf |access-date=25 February 2023 |website=Foundation of Louis de Broglie |edition=English translation by A.F. Kracklauer, 2004.}}</ref> He suggested that an electron around a nucleus could be thought of as being a [[standing wave]] 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 ([[wave packet]]s) that move with a [[group velocity]] and have an [[Effective mass (solid-state physics)|effective mass]]. Both of these depend upon the energy, which in turn connects to the [[Wave vector|wavevector]] and the relativistic formulation of [[Albert Einstein]] a few years before.

Following de Broglie's proposal of wave–particle duality of electrons, in 1925 to 1926, [[Erwin Schrödinger]] developed the wave equation of motion for electrons. This rapidly became part of what was called by Schrödinger ''undulatory mechanics'',<ref name="Schroedinger">{{Cite journal |last=Schrödinger |first=E. |date=1926 |title=An Undulatory Theory of the Mechanics of Atoms and Molecules |url=https://link.aps.org/doi/10.1103/PhysRev.28.1049 |journal=Physical Review |language=en |volume=28 |issue=6 |pages=1049–1070 |bibcode=1926PhRv...28.1049S |doi=10.1103/PhysRev.28.1049 |issn=0031-899X|url-access=subscription }}</ref> now called the [[Schrödinger equation]] and also "wave mechanics".

In 1926, [[Max Born]] 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 [[Clinton Davisson]] 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.<ref>{{Cite journal |last=Gehrenbeck |first=Richard K. |date=1978-01-01 |title=Electron diffraction: fifty years ago |url=https://doi.org/10.1063/1.3001830 |journal=Physics Today |volume=31 |issue=1 |pages=34–41 |doi=10.1063/1.3001830 |issn=0031-9228|url-access=subscription }}</ref>

In 1927, the wave nature of electrons was empirically confirmed by two experiments. The [[Davisson–Germer experiment]] at Bell Labs measured electrons scattered from [[Nickel|Ni metal]] surfaces.<ref>{{Cite journal | author=[[C. Davisson]] and [[L. H. Germer]] | s2cid=4104602 | title=The scattering of electrons by a single crystal of nickel | journal=Nature | year=1927 | volume=119 | pages=558–560 | doi=10.1038/119558a0|bibcode = 1927Natur.119..558D | issue=2998|ref=none | url=https://commons.wikimedia.org/wiki/File:The_Scattering_of_Electrons_by_a_Single_Crystal_of_Nickel.pdf}}</ref><ref name="DG12">{{Cite journal |last1=Davisson |first1=C. |last2=Germer |first2=L. H. |date=1927 |title=Diffraction of Electrons by a Crystal of Nickel |journal=Physical Review |volume=30 |issue=6 |pages=705–740 |bibcode=1927PhRv...30..705D |doi=10.1103/physrev.30.705 |issn=0031-899X |doi-access=free}}</ref><ref>{{Cite journal |last1=Davisson |first1=C. |last2=Germer |first2=L. H. |date=1927 |title=Diffraction of Electrons by a Crystal of Nickel |journal=Physical Review |language=en |volume=30 |issue=6 |pages=705–740 |bibcode=1927PhRv...30..705D |doi=10.1103/PhysRev.30.705 |issn=0031-899X |doi-access=free}}</ref><ref name="DG22">{{Cite journal |last1=Davisson |first1=C. J. |last2=Germer |first2=L. H. |date=1928 |title=Reflection of Electrons by a Crystal of Nickel |journal=Proceedings of the National Academy of Sciences |language=en |volume=14 |issue=4 |pages=317–322 |bibcode=1928PNAS...14..317D |doi=10.1073/pnas.14.4.317 |issn=0027-8424 |pmc=1085484 |pmid=16587341 |doi-access=free}}</ref><ref name=":02">{{Cite journal |last1=Davisson |first1=C. J. |last2=Germer |first2=L. H. |date=1928 |title=Reflection and Refraction of Electrons by a Crystal of Nickel |journal=Proceedings of the National Academy of Sciences |language=en |volume=14 |issue=8 |pages=619–627 |bibcode=1928PNAS...14..619D |doi=10.1073/pnas.14.8.619 |issn=0027-8424 |pmc=1085652 |pmid=16587378 |doi-access=free}}</ref> [[George Paget Thomson]] and Alexander Reid at Cambridge University scattered electrons through thin [[nickel]] films and observed concentric diffraction rings.<ref>{{Cite journal |last1=Thomson |first1=G. P. |last2=Reid |first2=A. |date=1927 |title=Diffraction of Cathode Rays by a Thin Film |journal=Nature |language=en |volume=119 |issue=3007 |pages=890 |bibcode=1927Natur.119Q.890T |doi=10.1038/119890a0 |issn=0028-0836 |s2cid=4122313 |doi-access=free}}</ref> Alexander Reid, who was Thomson's graduate student, performed the first experiments,<ref>{{Cite journal |last=Reid |first=Alexander |date=1928 |title=The diffraction of cathode rays by thin celluloid films |journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character |language=en |volume=119 |issue=783 |pages=663–667 |bibcode=1928RSPSA.119..663R |doi=10.1098/rspa.1928.0121 |issn=0950-1207 |s2cid=98311959 |doi-access=free}}</ref> but he died soon after in a motorcycle accident<ref>{{Cite journal |last=Navarro |first=Jaume |date=2010 |title=Electron diffraction chez Thomson: early responses to quantum physics in Britain |url=https://www.cambridge.org/core/product/identifier/S0007087410000026/type/journal_article |journal=The British Journal for the History of Science |language=en |volume=43 |issue=2 |pages=245–275 |doi=10.1017/S0007087410000026 |issn=0007-0874 |s2cid=171025814|url-access=subscription }}</ref> and is rarely mentioned. These experiments were rapidly followed by the first non-relativistic diffraction model for electrons by [[Hans Bethe]]<ref name="Bethe">{{Cite journal |last=Bethe |first=H. |date=1928 |title=Theorie der Beugung von Elektronen an Kristallen |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.19283921704 |journal=Annalen der Physik |language=de |volume=392 |issue=17 |pages=55–129 |doi=10.1002/andp.19283921704|bibcode=1928AnP...392...55B |url-access=subscription }}</ref> based upon the [[Schrödinger equation]], which is very close to how electron diffraction is now described. Significantly, Davisson and Germer noticed<ref name="DG22" /><ref name=":02" /> that their results could not be interpreted using a [[Bragg's law]] approach as the positions were systematically different; the approach of Bethe,<ref name="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 diffraction experiments.<ref>{{Cite web |title=The Nobel Prize in Physics 1937 |url=https://www.nobelprize.org/prizes/physics/1937/summary/ |access-date=2024-03-18 |website=NobelPrize.org |language=en-US}}</ref> Similar crystal diffraction experiments were carried out by [[Otto Stern]] 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.