Editing Wolfgang Pauli (section)

== Scientific research ==
{{Quantum mechanics}}
[[File:The physicists Paul Dirac, Wolfgang Pauli and Rudolf Peierls, c 1953. (9660575591).jpg|thumb|[[Paul Dirac]], Wolfgang Pauli and [[Rudolf Peierls]], {{Circa|1953}}]]
Pauli made many important contributions as a physicist, primarily in the field of [[quantum mechanics]]. He seldom published papers, preferring lengthy correspondences with colleagues such as [[Niels Bohr]] from the [[University of Copenhagen]] in Denmark and [[Werner Heisenberg]], with whom he had close friendships. Many of his ideas and results were never published and appeared only in his letters, which were often copied and circulated by their recipients. In 1921 Pauli worked with Bohr to create the [[Aufbau Principle]], which described building up electrons in shells based on the German word for building up, as Bohr was also fluent in German.

Pauli proposed in 1924 a new quantum degree of freedom (or [[quantum number]]) with two possible values, to resolve inconsistencies between observed molecular spectra and the developing theory of quantum mechanics. He formulated the Pauli exclusion principle, perhaps his most important work, which stated that no two electrons could exist in the same quantum state, identified by four quantum numbers including his new two-valued degree of freedom. The idea of spin originated with [[Ralph Kronig]]. A year later, [[George Uhlenbeck]] and [[Samuel Goudsmit]] identified Pauli's new degree of freedom as [[electron]] [[Spin (physics)|spin]], in which Pauli for a very long time wrongly refused to believe.<ref>{{cite web|last=Goudsmit|first=S.A.|author2=translated by van der Waals, J.H. |title=The discovery of the electron spin|url=https://ilorentz.org/history/spin/goudsmit.html}}</ref>

In 1926, shortly after Heisenberg published the [[Matrix mechanics|matrix theory]] of modern [[quantum mechanics]], Pauli used it to derive the observed [[spectrum]] of the [[hydrogen atom]]. This result was important in securing credibility for Heisenberg's theory.

Pauli introduced the 2×2 [[Pauli matrices]] as a basis of spin operators, thus solving the nonrelativistic theory of spin. This work, including the [[Pauli equation]], is sometimes said to have influenced [[Paul Dirac]] in his creation of the [[Dirac equation]] for the [[relativistic particle|relativistic]] electron, though Dirac said that he invented these same matrices himself independently at the time. Dirac invented similar but larger (4x4) spin matrices for use in his relativistic treatment of [[Fermion|fermionic spin]].

In 1930, Pauli considered the problem of [[beta decay]]. In a letter of 4 December to [[Lise Meitner]] ''et al.'', beginning, "[[Electron neutrino#Pauli's letter|Dear radioactive ladies and gentlemen]]", he proposed the existence of a hitherto unobserved neutral particle with a small mass, no greater than 1% the mass of a proton, to explain the continuous spectrum of beta decay. In 1934, [[Enrico Fermi]] incorporated the particle, which he called a [[neutrino]], "little neutral one" in Fermi's native Italian, into his theory of beta decay. The neutrino was first confirmed experimentally in 1956 by [[Frederick Reines]] and [[Clyde Cowan]], two and a half years before Pauli's death. On receiving the news, he replied by telegram: "Thanks for message. Everything comes to him who knows how to wait. Pauli."<ref>{{cite journal|last=Enz|first=Charles|author2=Meyenn, Karl von|title=Wolfgang Pauli, A Biographical Introduction|journal=Writings on Physics and Philosophy|publisher=Springer-Verlag|page=19|year=1994}}</ref>

In 1940, Pauli re-derived the [[spin-statistics theorem]], a critical result of quantum field theory that states that particles with half-integer spin are [[fermion]]s, while particles with integer spin are [[boson]]s.

In 1949, he published a paper on [[Pauli–Villars regularization]]: regularization is the term for techniques that modify infinite mathematical integrals to make them finite during calculations, so that one can identify whether the intrinsically infinite quantities in the theory (mass, charge, wavefunction) form a finite and hence calculable set that can be redefined in terms of their experimental values, which criterion is termed [[renormalization]], and which removes infinities from [[quantum field theory|quantum field theories]], but also importantly allows the calculation of higher-order corrections in perturbation theory.

Pauli made repeated criticisms of the [[modern synthesis (20th century)|modern synthesis]] of [[evolutionary biology]],<ref>{{cite journal|last=Pauli|first=W.|title=Naturwissenschaftliche und erkenntnistheoretische Aspekte der Ideen vom Unbewussten|journal=Dialectica|volume=8|issue=4|pages=283–301|doi= 10.1111/j.1746-8361.1954.tb01265.x|year=1954}}</ref><ref>{{cite journal|last=Atmanspacher|first=H.|author2=Primas, H.|title=Pauli's ideas on mind and matter in the context of contemporary science|journal=Journal of Consciousness Studies|volume=13|issue=3|pages=5–50|year=2006|url=http://www.igpp.de/english/tda/pdf/paulijcs8.pdf|access-date=12 February 2009|url-status=dead|archive-url=https://web.archive.org/web/20090319155642/http://www.igpp.de/english/tda/pdf/paulijcs8.pdf|archive-date=19 March 2009}}</ref> and his contemporary admirers point to modes of [[epigenetics|epigenetic inheritance]] as supporting his arguments.<ref>[http://www.solid.ethz.ch/pauli-conference/thematic.htm Conference on Wolfgang Pauli's Philosophical Ideas and Contemporary Science] {{Webarchive|url=https://web.archive.org/web/20140910103419/http://www.solid.ethz.ch/pauli-conference/thematic.htm|date=10 September 2014}} organised by [[ETH]] 20–25 May 2007. The abstract of a paper discussing this by Richard Jorgensen is here [http://www.solid.ethz.ch/pauli-conference/abstracts.htm] {{Webarchive|url=https://web.archive.org/web/20150924103559/http://www.solid.ethz.ch/pauli-conference/abstracts.htm|date=24 September 2015}}</ref>

[[Paul Drude]] in 1900 proposed the first theoretical model for a [[classical mechanics|classical]] [[electron]] moving through a metallic solid. Drude's classical model was also augmented by Pauli and other physicists.  Pauli realized that the free electrons in metal must obey the [[Fermi–Dirac statistics]].  Using this idea, he developed the theory of [[paramagnetism]] in 1926. Pauli said, "Festkörperphysik ist eine Schmutzphysik"—solid-state physics is the physics of dirt.<ref name="AIP Publishing 2018 p. ">{{cite journal | title=Commentary: Condensed matter's image problem | journal=Physics Today | publisher=AIP Publishing | date=19 December 2018 | issn=1945-0699 | doi=10.1063/pt.6.3.20181219a | page=30800 | last1=Natelson | first1=Douglas | issue=12 | bibcode=2018PhT..2018l0800N }}</ref>

Pauli was elected a [[List of Fellows of the Royal Society elected in 1953|Foreign Member of the Royal Society (ForMemRS) in 1953]] and president of the [[Swiss Physical Society]] in 1955 for two years.<ref name="peierls" /> In 1958 he became a foreign member of the [[Royal Netherlands Academy of Arts and Sciences]].<ref>{{cite web|title=Wolfgang Ernst Pauli (1900–1958)|url=http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00002258|access-date=26 July 2015|publisher=Royal Netherlands Academy of Arts and Sciences}}</ref>