Editing Electron (section)

=== Quantum mechanics ===
{{See also|History of quantum mechanics}}
{{further|#Quantum properties}}
In his 1924 dissertation ''{{lang|fr|Recherches sur la théorie des quanta}}'' (Research on Quantum Theory), French physicist [[Louis de Broglie]] hypothesized that all matter can be represented as a [[Matter wave|de Broglie wave]] in the manner of [[light]].<ref name="de_broglie">
{{cite web
 | last = de Broglie
 | first = L.
 | year = 1929
 | title = Nobel Lecture: The Wave Nature of the Electron
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | access-date = 2008-08-30
 | df = dmy-all
 | archive-date = 2008-10-04
 | archive-url = https://web.archive.org/web/20081004022001/http://nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf
 | url-status = live
}}</ref> That is, under the appropriate conditions, electrons and other matter would show properties of either particles or waves. The [[Corpuscular theory of light|corpuscular properties]] of a particle are demonstrated when it is shown to have a localized position in space along its trajectory at any given moment.<ref>
{{cite book
 | last = Falkenburg
 | first = B.
 | year = 2007
 | title = Particle Metaphysics: A Critical Account of Subatomic Reality
 | url = https://books.google.com/books?id=EbOz5I9RNrYC&pg=PA85
 | page = 85
 | publisher = [[Springer Science+Business Media|Springer]]
 | isbn = 978-3-540-33731-7
 | bibcode = 2007pmca.book.....F
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082417/https://books.google.com/books?id=EbOz5I9RNrYC&pg=PA85
 | url-status = live
}}</ref> The wave-like nature of light is displayed, for example, when a beam of light is passed through parallel slits thereby creating [[Interference (wave propagation)|interference]] patterns. In 1927, [[George Paget Thomson]] and Alexander Reid discovered the interference effect was produced when a beam of electrons was passed through thin celluloid foils and later metal films, and by American physicists [[Clinton Davisson]] and [[Lester Germer]] by the reflection of electrons from a crystal of [[nickel]].<ref>
{{cite web
 | last = Davisson
 | first = C.
 | year = 1937
 | title = Nobel Lecture: The Discovery of Electron Waves
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1937/davisson-lecture.pdf
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | access-date = 2008-08-30
 | df = dmy-all
 | archive-date = 2008-07-09
 | archive-url = https://web.archive.org/web/20080709090839/http://nobelprize.org/nobel_prizes/physics/laureates/1937/davisson-lecture.pdf
 | url-status = live
}}</ref> Alexander Reid, who was Thomson's graduate student, performed the first experiments 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 |s2cid=171025814 |issn=0007-0874}}</ref> and is rarely mentioned.

[[File:Orbital s1.png|right|thumb|alt=A spherically symmetric blue cloud that decreases in intensity from the center outward|In quantum mechanics, the behavior of an electron in an atom is described by an [[atomic orbital|orbital]], which is a probability distribution rather than an orbit. In the figure, the shading indicates the relative probability to "find" the electron, having the energy corresponding to the given [[quantum number]]s, at that point.]]
De Broglie's prediction of a wave nature for electrons led [[Erwin Schrödinger]] to postulate a wave equation for electrons moving under the influence of the nucleus in the atom. In 1926, this equation, the [[Schrödinger equation]], successfully described how electron waves propagated.<ref>
{{cite journal
 | last = Schrödinger | first = E.
 | year = 1926
 | title = Quantisierung als Eigenwertproblem
 | journal = [[Annalen der Physik]]
 | volume = 385 | issue = 13 | pages = 437–490
 | bibcode = 1926AnP...385..437S
 | doi = 10.1002/andp.19263851302
 |language=de
}}</ref> Rather than yielding a solution that determined the location of an electron over time, this wave equation also could be used to predict the probability of finding an electron near a position, especially a position near where the electron was bound in space, for which the electron wave equations did not change in time. This approach led to a second formulation of [[quantum mechanics]] (the first by Heisenberg in 1925), and solutions of Schrödinger's equation, like Heisenberg's, provided derivations of the energy states of an electron in a hydrogen atom that were equivalent to those that had been derived first by Bohr in 1913, and that were known to reproduce the hydrogen spectrum.<ref>
{{cite book
 | last = Rigden
 | first = J.S.
 | year = 2003
 | title = Hydrogen
 | url = https://books.google.com/books?id=FhFxn_lUvz0C&pg=PT66
 | publisher = Harvard University Press
 | pages = 59–86
 | isbn = 978-0-674-01252-3
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082407/https://books.google.com/books?id=FhFxn_lUvz0C&pg=PT66
 | url-status = live
}}</ref> Once spin and the interaction between multiple electrons were describable, quantum mechanics made it possible to predict the configuration of electrons in atoms with atomic numbers greater than hydrogen.<ref>
{{cite book
 | last = Reed
 | first = B.C.
 | year = 2007
 | title = Quantum Mechanics
 | url = https://books.google.com/books?id=4sluccbpwjsC&pg=PA275
 | pages = 275–350
 | publisher = [[Jones & Bartlett Learning|Jones & Bartlett Publishers]]
 | isbn = 978-0-7637-4451-9
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082419/https://books.google.com/books?id=4sluccbpwjsC&pg=PA275
 | url-status = live
}}</ref>

In 1928, building on Wolfgang Pauli's work, [[Paul Dirac]] produced a model of the electron&nbsp;– the [[Dirac equation]], consistent with [[Principle of relativity|relativity]] theory, by applying relativistic and symmetry considerations to the [[Hamiltonian (quantum mechanics)|hamiltonian]] formulation of the quantum mechanics of the electromagnetic field.<ref>
{{cite journal
 |last         = Dirac
 |first        = P.A.M.
 |year         = 1928
 |title        = The Quantum Theory of the Electron
 |journal      = [[Proceedings of the Royal Society#Proceedings of the Royal Society A|Proceedings of the Royal Society A]]
 |volume       = 117
 |issue        = 778
 |pages        = 610–624
 |doi          = 10.1098/rspa.1928.0023
 |bibcode      = 1928RSPSA.117..610D
 |url          = https://rspa.royalsocietypublishing.org/content/royprsa/117/778/610.full.pdf
 |doi-access   = free
 |access-date  = 2022-02-24
 |archive-date = 2018-11-25
 |archive-url  = https://web.archive.org/web/20181125224103/http://rspa.royalsocietypublishing.org/content/royprsa/117/778/610.full.pdf
 |url-status   = live
}}</ref> In order to resolve some problems within his relativistic equation, Dirac developed in 1930 a model of the vacuum as an infinite sea of particles with negative energy, later dubbed the [[Dirac sea]]. This led him to predict the existence of a positron, the [[antimatter]] counterpart of the electron.<ref>
{{cite web
 | last = Dirac
 | first = P.A.M.
 | year = 1933
 | title = Nobel Lecture: Theory of Electrons and Positrons
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1933/dirac-lecture.pdf
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | access-date = 2008-11-01
 | df = dmy-all
 | archive-date = 2008-07-23
 | archive-url = https://web.archive.org/web/20080723220816/http://nobelprize.org/nobel_prizes/physics/laureates/1933/dirac-lecture.pdf
 | url-status = live
}}</ref> This particle was discovered in 1932 by [[Carl David Anderson|Carl Anderson]], who proposed calling standard electrons ''negatrons'' and using ''electron'' as a generic term to describe both the positively and negatively charged variants.<ref>{{Cite journal |last=Anderson |first=Carl D. |date=1933-03-15 |title=The Positive Electron |journal=Physical Review |language=en |volume=43 |issue=6 |pages=491–494 |doi=10.1103/PhysRev.43.491 |bibcode=1933PhRv...43..491A |issn=0031-899X|doi-access=free }}</ref>

In 1947, [[Willis Lamb]], working in collaboration with graduate student [[Robert Retherford]], found that certain quantum states of the hydrogen atom, which should have the same energy, were shifted in relation to each other; the difference came to be called the [[Lamb shift]]. About the same time, [[Polykarp Kusch]], working with [[Henry M. Foley]], discovered the magnetic moment of the electron is slightly larger than predicted by Dirac's theory. This small difference was later called [[anomalous magnetic dipole moment]] of the electron. This difference was later explained by the theory of [[quantum electrodynamics]], developed by [[Sin-Itiro Tomonaga]], [[Julian Schwinger]] and
[[Richard Feynman]] in the late 1940s.<ref>
{{cite web
 | title = The Nobel Prize in Physics 1965
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1965/
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | access-date = 2008-11-04
 | df = dmy-all
 | archive-date = 2008-10-24
 | archive-url = https://web.archive.org/web/20081024052537/http://nobelprize.org/nobel_prizes/physics/laureates/1965/
 | url-status = live
}}</ref>