Editing Quantum mechanics (section)

== History ==
{{Main|History of quantum mechanics|Atomic theory}}

Quantum mechanics was developed in the early decades of the 20th century, driven by the need to explain phenomena that, in some cases, had been observed in earlier times. Scientific inquiry into the wave nature of light began in the 17th and 18th centuries, when scientists such as [[Robert Hooke]], [[Christiaan Huygens]] and [[Leonhard Euler]] proposed a wave theory of light based on experimental observations.<ref name="Born & Wolf">{{cite book |first1=Max |last1=Born |author-link1=Max Born |first2=Emil |last2=Wolf |author-link2=Emil Wolf |title=Principles of Optics |title-link=Principles of Optics |year=1999 |publisher=Cambridge University Press |isbn=0-521-64222-1 |oclc=1151058062}}</ref> In 1803 English [[polymath]] [[Thomas Young (scientist)|Thomas Young]] described the famous [[Young's interference experiment|double-slit experiment]].<ref>{{Cite journal |last=Scheider |first=Walter |date=April 1986 |title=Bringing one of the great moments of science to the classroom |url=http://www.cavendishscience.org/phys/tyoung/tyoung.htm |journal=[[The Physics Teacher]] |volume=24 |issue=4 |pages=217–219 |doi=10.1119/1.2341987 |bibcode=1986PhTea..24..217S |issn=0031-921X}}</ref> This experiment played a major role in the general acceptance of the [[wave theory of light]].

During the early 19th century, [[chemistry|chemical]] research by [[John Dalton]] and [[Amedeo Avogadro]] lent weight to the [[atomic theory]] of matter, an idea that [[James Clerk Maxwell]], [[Ludwig Boltzmann]] and others built upon to establish the [[kinetic theory of gases]]. The successes of kinetic theory gave further credence to the idea that matter is composed of atoms, yet the theory also had shortcomings that would only be resolved by the development of quantum mechanics.<ref name="Feynman-kinetic-theory">{{cite book |last1=Feynman |first1=Richard |last2=Leighton |first2=Robert |last3=Sands |first3=Matthew |title=The Feynman Lectures on Physics |volume=1 |publisher=California Institute of Technology |date=1964 |url=https://feynmanlectures.caltech.edu/I_40.html |access-date=30 September 2021}} Reprinted, Addison-Wesley, 1989, {{isbn|978-0-201-50064-6}} </ref> While the early conception of atoms from [[Greek philosophy]] had been that they were indivisible units{{snd}}the word "atom" deriving from the [[Greek language|Greek]] for 'uncuttable'{{snd}}the 19th century saw the formulation of hypotheses about subatomic structure. One important discovery in that regard was [[Michael Faraday]]'s 1838 observation of a glow caused by an electrical discharge inside a glass tube containing gas at low pressure. [[Julius Plücker]], [[Johann Wilhelm Hittorf]] and [[Eugen Goldstein]] carried on and improved upon Faraday's work, leading to the identification of [[cathode rays]], which [[J. J. Thomson]] found to consist of subatomic particles that would be called electrons.<ref>{{citation |first=Andre |last=Martin |contribution=Cathode Ray Tubes for Industrial and Military Applications |editor-last=Hawkes |editor-first=Peter |title=Advances in Electronics and Electron Physics, Volume 67 |publisher=Academic Press |year=1986 |isbn=978-0-08-057733-3 |page=183 |quote="Evidence for the existence of "cathode-rays" was first found by Plücker and Hittorf ..."}}</ref><ref>{{Cite book |last=Dahl |first=Per F. |url=https://books.google.com/books?id=xUzaWGocMdMC |title=Flash of the Cathode Rays: A History of J. J. Thomson's Electron |year=1997 |publisher=CRC Press |isbn=978-0-7503-0453-5 |pages=47–57}}</ref>
[[File:Max Planck (1858-1947).jpg|thumb|upright|[[Max Planck]] is considered the father of the quantum theory.]]

The [[black-body radiation]] problem was discovered by [[Gustav Kirchhoff]] in 1859. In 1900, Max Planck proposed the hypothesis that energy is radiated and absorbed in discrete "quanta" (or energy packets), yielding a calculation that precisely matched the observed patterns of black-body radiation.<ref>{{cite book |first1=J. |last1=Mehra |author-link1=Jagdish Mehra |first2=H. |last2=Rechenberg |title=The Historical Development of Quantum Theory, Vol. 1: The Quantum Theory of Planck, Einstein, Bohr and Sommerfeld. Its Foundation and the Rise of Its Difficulties (1900–1925) |location=New York |publisher=Springer-Verlag |year=1982 |isbn=978-0-387-90642-3}}</ref> The word ''quantum'' derives from the [[Latin]], meaning "how great" or "how much".<ref>{{cite dictionary |title=Quantum |url=http://www.merriam-webster.com/dictionary/quantum |access-date=18 August 2012 |dictionary=Merriam-Webster Dictionary |url-status=live |archive-url=https://web.archive.org/web/20121026104456/http://www.merriam-webster.com/dictionary/quantum |archive-date=Oct 26, 2012}}</ref> According to Planck, quantities of energy could be thought of as divided into "elements" whose size (''E'') would be proportional to their [[frequency]] (''ν''):
<math display=block> E = h \nu\ </math>,
where ''h'' is the [[Planck constant]]. Planck cautiously insisted that this was only an aspect of the processes of absorption and emission of radiation and was not the <em>physical reality</em> of the radiation.<ref>{{cite book |last=Kuhn |first=T. S. |title=Black-body theory and the quantum discontinuity 1894–1912 |publisher=Clarendon Press |year=1978 |isbn=978-0-19-502383-1 |location=Oxford |author-link=Thomas Samuel Kuhn}}</ref> In fact, he considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizable discovery.<ref name="Kragh">{{cite magazine |last=Kragh |first=Helge |author-link=Helge Kragh |title=Max Planck: the reluctant revolutionary |date=1 December 2000 |url=https://physicsworld.com/a/max-planck-the-reluctant-revolutionary/ |magazine=[[Physics World]] |access-date=12 December 2020}}</ref> However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis [[local realism|realistically]] and used it to explain the [[photoelectric effect]], in which shining light on certain materials can eject electrons from the material. Niels Bohr then developed Planck's ideas about radiation into a [[Bohr model|model of the hydrogen atom]] that successfully predicted the [[spectral line]]s of hydrogen.<ref>{{cite book |last=Stachel |first=John |title=Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle |author-link=John Stachel |year=2009 |chapter=Bohr and the Photon |series=The Western Ontario Series in Philosophy of Science |volume=73 |location=Dordrecht |publisher=Springer |pages=69–83 |doi=10.1007/978-1-4020-9107-0_5 |isbn=978-1-4020-9106-3}}</ref> Einstein further developed this idea to show that an [[electromagnetic wave]] such as light could also be described as a particle (later called the photon), with a discrete amount of energy that depends on its frequency.<ref>{{cite journal |last=Einstein |first=Albert |year=1905 |title=Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt |trans-title=On a heuristic point of view concerning the production and transformation of light |journal=[[Annalen der Physik]] |volume=17 |issue=6 |pages=132–148 |bibcode=1905AnP...322..132E |doi=10.1002/andp.19053220607 |doi-access=free |language=de}} Reprinted in {{cite book |title=The Collected Papers of Albert Einstein |publisher=Princeton University Press |year=1989 |editor-last=Stachel |editor-first=John |editor-link=John Stachel |volume=2 |pages=149–166 |language=de}} See also "Einstein's early work on the quantum hypothesis", ibid. pp. 134–148.</ref> In his paper "On the Quantum Theory of Radiation", Einstein expanded on the interaction between energy and matter to explain the absorption and emission of energy by atoms. Although overshadowed at the time by his general theory of relativity, this paper articulated the mechanism underlying the stimulated emission of radiation,<ref>{{cite journal |first=Albert |last=Einstein |author-link=Albert Einstein |year=1917 |title=Zur Quantentheorie der Strahlung |trans-title=On the Quantum Theory of Radiation |language=de |journal=[[Physikalische Zeitschrift]] |volume=18 |pages=121–128 |bibcode=1917PhyZ...18..121E}} Translated in {{cite book |title=The Old Quantum Theory |date=1967 |pages=167–183 |chapter=On the Quantum Theory of Radiation |publisher=Elsevier |doi=10.1016/b978-0-08-012102-4.50018-8 |isbn=978-0-08-012102-4 |last1=Einstein |first1=A.}}</ref> which became the basis of the laser.<ref>{{cite news |first=Philip |last=Ball |url=https://physicsworld.com/a/a-century-ago-einstein-sparked-the-notion-of-the-laser/ |title=A century ago Einstein sparked the notion of the laser |author-link=Philip Ball |work=[[Physics World]] |date=2017-08-31 |access-date=2024-03-23}}</ref>

[[File:Solvay conference 1927.jpg|left|thumb|upright=1.4|The 1927 [[Solvay Conference]] in [[Brussels]] was the fifth world physics conference.]]
This phase is known as the [[old quantum theory]]. Never complete or self-consistent, the old quantum theory was rather a set of [[heuristic]] corrections to classical mechanics.<ref name="terHaar">{{cite book |last=ter Haar |first=D. |url=https://archive.org/details/oldquantumtheory0000haar |title=The Old Quantum Theory |publisher=Pergamon Press |year=1967 |isbn=978-0-08-012101-7 |lccn=66-29628 |pages=3–75 |url-access=registration}}</ref><ref>{{cite SEP |title=Bohr's Correspondence Principle |date=2020-08-13 |author-first1=Alisa |author-last1=Bokulich |author-first2=Peter |author-last2=Bokulich |url-id=bohr-correspondence}}</ref> The theory is now understood as a [[WKB approximation#Application to the Schrödinger equation|semi-classical approximation]] to modern quantum mechanics.<ref>{{cite encyclopedia |title=Semi-classical approximation |url=https://www.encyclopediaofmath.org/index.php?title=Semi-classical_approximation |access-date=1 February 2020 |encyclopedia=Encyclopedia of Mathematics}}</ref><ref>{{cite book |last1=Sakurai |first1=J. J. |title=Modern Quantum Mechanics |title-link=Modern Quantum Mechanics |last2=Napolitano |first2=J. |publisher=Pearson |year=2014 |isbn=978-1-292-02410-3 |chapter=Quantum Dynamics |oclc=929609283 |author-link1=J. J. Sakurai}}</ref> Notable results from this period include, in addition to the work of Planck, Einstein and Bohr mentioned above, Einstein and [[Peter Debye]]'s work on the [[specific heat]] of solids, Bohr and [[Hendrika Johanna van Leeuwen]]'s [[Bohr–Van Leeuwen theorem|proof]] that classical physics cannot account for [[diamagnetism]], and [[Arnold Sommerfeld]]'s extension of the Bohr model to include special-relativistic effects.<ref name="terHaar" /><ref name=Aharoni>{{cite book |last=Aharoni |first=Amikam |author-link=Amikam Aharoni |title=Introduction to the Theory of Ferromagnetism |publisher=[[Clarendon Press]] |year=1996 |isbn=0-19-851791-2 |pages=[https://archive.org/details/introductiontoth00ahar/page/6 6–7] |url=https://archive.org/details/introductiontoth00ahar/page/6}}</ref>

In the mid-1920s quantum mechanics was developed to become the standard formulation for atomic physics. In 1923, the French physicist [[Louis de Broglie]] put forward his theory of matter waves by stating that particles can exhibit wave characteristics and vice versa. Building on de Broglie's approach, modern quantum mechanics was born in 1925, when the German physicists Werner Heisenberg, Max Born, and [[Pascual Jordan]]<ref name=Edwards79>David Edwards, "The Mathematical Foundations of Quantum Mechanics", ''Synthese'', Volume 42, Number 1/September, 1979, pp.&nbsp;1–70.</ref><ref name="Edwards81">David Edwards, "The Mathematical Foundations of Quantum Field Theory: Fermions, Gauge Fields, and Super-symmetry, Part I: Lattice Field Theories", ''International Journal of Theoretical Physics'', Vol. 20, No. 7 (1981).</ref> developed [[matrix mechanics]] and the Austrian physicist Erwin Schrödinger invented [[Schrödinger equation|wave mechanics]]. Born introduced the probabilistic interpretation of Schrödinger's wave function in July 1926.<ref>{{Cite journal |last=Bernstein |first=Jeremy |author-link=Jeremy Bernstein |date=November 2005 |title=Max Born and the quantum theory |journal=[[American Journal of Physics]] |volume=73 |issue=11 |pages=999–1008 |doi=10.1119/1.2060717 |bibcode=2005AmJPh..73..999B |issn=0002-9505 |doi-access=free}}</ref> Thus, the entire field of quantum physics emerged, leading to its wider acceptance at the Fifth [[Solvay Conference]] in 1927.<ref name="pais1997">{{cite book |last=Pais |first=Abraham |author-link=Abraham Pais |title=A Tale of Two Continents: A Physicist's Life in a Turbulent World |year=1997 |publisher=Princeton University Press |location=Princeton, New Jersey |isbn=0-691-01243-1 |url-access=registration |url=https://archive.org/details/taleoftwocontine00pais}}</ref>

By 1930, quantum mechanics had been further unified and formalized by [[David Hilbert]], Paul Dirac and [[John von Neumann]]<ref>{{cite journal |last=Van Hove |first=Leon |title=Von Neumann's contributions to quantum mechanics |journal=[[Bulletin of the American Mathematical Society]] |year=1958 |volume=64 |issue=3 |pages=Part 2:95–99 |url=https://www.ams.org/journals/bull/1958-64-03/S0002-9904-1958-10206-2/S0002-9904-1958-10206-2.pdf |doi=10.1090/s0002-9904-1958-10206-2 |doi-access=free |url-status=live |archive-url=https://web.archive.org/web/20240120073106/https://www.ams.org/journals/bull/1958-64-03/S0002-9904-1958-10206-2/S0002-9904-1958-10206-2.pdf |archive-date=Jan 20, 2024}}</ref> with greater emphasis on [[measurement in quantum mechanics|measurement]], the statistical nature of our knowledge of reality, and [[Interpretations of quantum mechanics|philosophical speculation about the 'observer']]. It has since permeated many disciplines, including quantum chemistry, [[quantum electronics]], [[quantum optics]], and [[quantum information science]]. It also provides a useful framework for many features of the modern [[periodic table of elements]], and describes the behaviors of [[atoms]] during [[chemical bond]]ing and the flow of electrons in computer [[semiconductor]]s, and therefore plays a crucial role in many modern technologies. While quantum mechanics was constructed to describe the world of the very small, it is also needed to explain some [[macroscopic]] phenomena such as [[superconductors]]<ref name="feynman2015">{{cite web |url=https://feynmanlectures.caltech.edu/III_21.html#Ch21-S5 |title=The Feynman Lectures on Physics Vol. III Ch. 21: The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity, 21-4 |quote=...it was long believed that the wave function of the Schrödinger equation would never have a macroscopic representation analogous to the macroscopic representation of the amplitude for photons. On the other hand, it is now realized that the phenomena of superconductivity presents us with just this situation. |last=Feynman |first=Richard |author-link=Richard Feynman |publisher=[[California Institute of Technology]] |access-date=24 November 2015 |url-status=live |archive-url=https://archive.today/20161215225248/http://www.feynmanlectures.caltech.edu/III_21.html%23Ch21-S5 |archive-date=15 Dec 2016}}</ref> and [[superfluid]]s.<ref>{{cite web |url=http://physics.berkeley.edu/sites/default/files/_/lt24_berk_expts_on_macro_sup_effects.pdf |first=Richard |last=Packard |year=2006 |title=Berkeley Experiments on Superfluid Macroscopic Quantum Effects |publisher=Physics Department, University of California, Berkeley |archive-url=https://web.archive.org/web/20151125112132/http://research.physics.berkeley.edu/packard/publications/Articles/LT24_Berk_expts_on_macro_sup_effects.pdf |archive-date=25 November 2015 |access-date=24 November 2015}}</ref>