Editing Semiclassical physics

{{Short description|Use of both classical and quantum physics to analyze a system}}
{{Use American English|date=January 2019}}{{No footnotes|date=November 2018}}

In [[physics]], '''semiclassical''' refers to a theory in which one part of a [[Physical system|system]] is described [[quantum mechanics|quantum mechanically]], whereas the other is treated [[classical mechanics|classically]]. For example, external [[field (physics)|field]]s will be constant, or when changing will be classically described. In general, it incorporates a development in [[exponent|power]]s of the [[Planck constant]], resulting in the classical physics of power 0, and the first nontrivial approximation to the power of (−1). In this case, there is a clear link between the quantum-mechanical system and the associated semi-classical and classical approximations, as it is similar in appearance to the transition from [[physical optics]] to [[geometric optics]].

== History ==
[[Max Planck]] was the first to introduce the idea of quanta of energy in 1900 while studying [[black-body radiation]]. In 1906, he was also the first to write that quantum theory should replicate classical mechanics at some limit, particularly if the [[Planck constant]] ''h'' were infinitesimal.<ref name=":0">{{Cite journal |last=Liboff |first=Richard L. |date=1984-02-01 |title=The correspondence principle revisited |url=https://pubs.aip.org/physicstoday/article/37/2/50/402950/The-correspondence-principle-revisitedThe-usual |journal=Physics Today |language=en |volume=37 |issue=2 |pages=50–55 |doi=10.1063/1.2916084 |issn=0031-9228|url-access=subscription }}</ref><ref name=":1">{{Cite book |last=Planck |first=Max |title=Vorlesungen über die Theorie der Warmestrahlung |publisher=Verlag von Johann Ambrosius Barth |year=1906 |publication-place=Leipzig}}</ref>  With this idea he showed that [[Planck's law]] for thermal radiation leads to the [[Rayleigh–Jeans law]], the classical prediction (valid for large [[wavelength]]).<ref name=":0" /><ref name=":1" />

== Instances ==

Some examples of a semiclassical approximation include:
* [[WKB approximation]]: electrons in classical external [[electromagnetic field]]s.
* [[semiclassical gravity]]: [[quantum field theory]] within a classical [[curved space|curved]] [[gravity|gravitational]] background (see [[general relativity]]).
* [[quantum chaos]]: quantization of classical [[Chaos theory|chaotic]] systems.
* magnetic properties of materials and astrophysical bodies under the effect of large magnetic fields (see for example [[De Haas–Van Alphen effect]])
* [[quantum field theory]]: only [[Feynman diagram]]s with at most a single closed loop (see for example [[one-loop Feynman diagram]]) are considered, which corresponds to the powers of the Planck constant.

== See also ==

* [[Bohr model]]
* [[Correspondence principle]]
* [[Classical limit]]
* [[Eikonal approximation]]
* [[Einstein–Brillouin–Keller method]]
* [[Old quantum theory]]

== References ==
{{reflist}}
* {{cite book|title=Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles|edition=2nd|author1=R. Resnick|author2=R. Eisberg|publisher=John Wiley & Sons|year=1985|isbn=978-0-471-87373-0|url-access=registration|url=https://archive.org/details/quantumphysicsof00eisb}}
* {{Cite book|title=Principles of Quantum Mechanics|author=P.A.M. Dirac|author-link=Paul Dirac|edition=4th|publisher=Clarendon Press|year=1981|isbn=978-0-19-852011-5}}
* {{cite book|title=General Principles of Quantum Mechanics|author=W. Pauli|author-link=Wolfgang Pauli|year=1980|publisher=Springer|isbn=3-540-09842-9}}
* {{cite book|author1=R.P. Feynman |author2=R.B. Leighton |author3=M. Sands | year = 1965 | title = Feynman Lectures on Physics|publisher=Addison-Wesley|volume=3| isbn = 0-201-02118-8}}
* {{cite book| author=C.B. Parker| title=McGraw-Hill Encyclopaedia of Physics| publisher=McGraw-Hill| edition=2nd| year=1994| isbn=0-07-051400-3| url-access=registration| url=https://archive.org/details/mcgrawhillencycl1993park}}

[[Category:Quantum mechanics]]
[[Category:Quantum field theory]]
[[Category:Quantum chemistry]]
[[Category:Theoretical chemistry]]
[[Category:Computational chemistry]]

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