# Quantum

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Minimum amount of a physical entity involved in an interaction

For other uses, see [Quantum (disambiguation)](/source/Quantum_(disambiguation)).

In [physics](/source/Physics), a **quantum** (pl.: **quanta**) is the minimum amount of any physical entity ([physical property](/source/Physical_property)) involved in an [interaction](/source/Fundamental_interaction). The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of [quantization](/source/Quantization_(physics))".[1] This means that the [magnitude](/source/Magnitude_(mathematics)) of the physical property can take on only [discrete](https://en.wiktionary.org/wiki/discrete) values consisting of [integer multiples](/source/Multiple_(mathematics)) of one quantum. For example, a [photon](/source/Photon) is a single quantum of [light](/source/Light) of a specific [frequency](/source/Frequency) (or of any other form of [electromagnetic radiation](/source/Electromagnetic_radiation)). Similarly, the energy of an [electron](/source/Electron) bound within an [atom](/source/Atom) is quantized and can exist only in certain discrete values.[2] Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom. Quantization is one of the foundations of the much broader physics of [quantum mechanics](/source/Quantum_mechanics). Quantization of [energy](/source/Energy) and its influence on how energy and matter interact ([quantum electrodynamics](/source/Quantum_electrodynamics)) is part of the fundamental framework for understanding and describing nature.

## Origin

German [physicist](/source/Physicist) and 1918 Nobel Prize for Physics recipient [Max Planck](/source/Max_Planck) (1858–1947)

The modern concept of the quantum in physics originates from December 14, 1900, when [Max Planck](/source/Max_Planck) reported his [findings](/source/Planck's_law) to the [German Physical Society](/source/German_Physical_Society). He showed that modelling harmonic oscillators with discrete energy levels resolved a longstanding problem in the theory of [blackbody radiation](/source/Blackbody_radiation).[3]: 15[4] In his report, Planck did not use the term *quantum* in the modern sense. Instead, he used the term *Elementarquantum* to refer to the "quantum of electricity", now known as the [elementary charge](/source/Elementary_charge). For the smallest unit of energy, he employed the term *Energieelement*, "energy element", rather than calling it a *quantum*.[5]

Shortly afterwards, in a paper published in *[Annalen der Physik](/source/Annalen_der_Physik)*,[6] Planck introduced the constant *h*, which he termed the "quantum of [action](/source/Action_(physics))" (*elementares Wirkungsquantum*) in 1906.[5] In this paper, Planck also reported more precise values for the elementary charge and the [Avogadro–Loschmidt number](/source/Avogadro_constant), the number of molecules in one [mole](/source/Mole_(unit)) of substance.[7] The constant *h* is now known as the [Planck constant](/source/Planck_constant). After his theory was validated, Planck was awarded the [Nobel Prize in Physics](/source/Nobel_Prize_in_Physics) for his discovery in 1918.[8]

In 1905 [Albert Einstein](/source/Albert_Einstein) suggested that [electromagnetic radiation](/source/Electromagnetic_radiation) exists in spatially localized packets which he called ["quanta of light"](/source/Photons) (*Lichtquanta*).[5][9] Einstein was able to use this hypothesis to recast Planck's treatment of the blackbody problem in a form that also explained the voltages observed in [Philipp Lenard](/source/Philipp_Lenard)'s experiments on the [photoelectric effect](/source/Photoelectric_effect).[3]: 23 Shortly thereafter, the term "energy quantum" was introduced for the quantity [*hν*](/source/Planck_relation).[10]

## Quantization

Main article: [Quantization (physics)](/source/Quantization_(physics))

While quantization was first discovered in [electromagnetic radiation](/source/Electromagnetic_radiation), it describes a fundamental aspect of energy not just restricted to photons.[11] In the attempt to bring theory into agreement with experiment, Max Planck postulated that electromagnetic energy is absorbed or emitted in discrete packets, or quanta.[12]

## See also

- [Introduction to quantum mechanics](/source/Introduction_to_quantum_mechanics)

- [History of quantum mechanics](/source/History_of_quantum_mechanics)

- [Quantum geometry](/source/Quantum_geometry_(condensed_matter))

## References

1. **[^](#cite_ref-1)** Wiener, N. (1966). *Differential Space, Quantum Systems, and Prediction*. Cambridge, Massachusetts: The Massachusetts Institute of Technology Press

1. **[^](#cite_ref-2)** Rovelli, Carlo (January 2017). *Reality is not what it seems: the elementary structure of things*. Translated by Carnell, Simon; Segre, Erica (1st American ed.). New York, New York: Riverhead Books. pp. 109–130. [ISBN](/source/ISBN_(identifier)) [978-0-7352-1392-0](https://en.wikipedia.org/wiki/Special:BookSources/978-0-7352-1392-0).

1. ^ [***a***](#cite_ref-Baggott-2013_3-0) [***b***](#cite_ref-Baggott-2013_3-1) Baggott, J. E. (2013). *The quantum story: a history in 40 moments* (Pbk ed.). Oxford [England]: Oxford University Press. [ISBN](/source/ISBN_(identifier)) [978-0-19-965597-7](https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-965597-7).

1. **[^](#cite_ref-Planck1901_4-0)** [Planck, M.](/source/Max_Planck) (1901). ["Ueber die Elementarquanta der Materie und der Elektricität"](https://zenodo.org/record/1423997). *[Annalen der Physik](/source/Annalen_der_Physik)* (in German). **309** (3): 564–566. [Bibcode](/source/Bibcode_(identifier)):[1901AnP...309..564P](https://ui.adsabs.harvard.edu/abs/1901AnP...309..564P). [doi](/source/Doi_(identifier)):[10.1002/andp.19013090311](https://doi.org/10.1002%2Fandp.19013090311). [Archived](https://web.archive.org/web/20230624230014/https://zenodo.org/record/1423997) from the original on 2023-06-24. Retrieved 2019-09-16 – via Zenodo.

1. ^ [***a***](#cite_ref-:0_5-0) [***b***](#cite_ref-:0_5-1) [***c***](#cite_ref-:0_5-2) ["Quantum"](https://doi.org/10.1093/OED/1164299139). *[Oxford English Dictionary](/source/Oxford_English_Dictionary)* (online ed.). Oxford University Press. 2007. [doi](/source/Doi_(identifier)):[10.1093/OED/1164299139](https://doi.org/10.1093%2FOED%2F1164299139). Retrieved 6 May 2025. (Subscription or [participating institution membership](https://www.oed.com/public/login/loggingin#withyourlibrary) required.)

1. **[^](#cite_ref-Planck01_6-0)** [Planck, Max](/source/Max_Planck) (1901), ["Ueber das Gesetz der Energieverteilung im Normalspectrum"](http://www.physik.uni-augsburg.de/annalen/history/historic-papers/1901_309_553-563.pdf) (PDF), *[Annalen der Physik](/source/Annalen_der_Physik)* (in German), **309** (3): 553–63, [Bibcode](/source/Bibcode_(identifier)):[1901AnP...309..553P](https://ui.adsabs.harvard.edu/abs/1901AnP...309..553P), [doi](/source/Doi_(identifier)):[10.1002/andp.19013090310](https://doi.org/10.1002%2Fandp.19013090310), [archived](https://web.archive.org/web/20120610124128/http://www.physik.uni-augsburg.de/annalen/history/historic-papers/1901_309_553-563.pdf) (PDF) from the original on 2012-06-10, retrieved 2008-12-15. English translations: - ["On the Law of Distribution of Energy in the Normal Spectrum"](https://web.archive.org/web/20080418002757/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html). Archived from [the original](http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html) on 2008-04-18. - ["On the Law of Distribution of Energy in the Normal Spectrum"](https://web.archive.org/web/20111006162543/http://theochem.kuchem.kyoto-u.ac.jp/Ando/planck1901.pdf) (PDF). Archived from [the original](http://theochem.kuchem.kyoto-u.ac.jp/Ando/planck1901.pdf) (PDF) on 2011-10-06. Retrieved 2011-10-13.

1. **[^](#cite_ref-7)** Klein, Martin J. (1961). "Max Planck and the beginnings of the quantum theory". *Archive for History of Exact Sciences*. **1** (5): 459–479. [doi](/source/Doi_(identifier)):[10.1007/BF00327765](https://doi.org/10.1007%2FBF00327765). [S2CID](/source/S2CID_(identifier)) [121189755](https://api.semanticscholar.org/CorpusID:121189755).

1. **[^](#cite_ref-8)** ["Max Planck Nobel Lecture"](https://www.nobelprize.org/prizes/physics/1918/planck/lecture/). [Archived](https://web.archive.org/web/20230714164215/https://www.nobelprize.org/prizes/physics/1918/planck/lecture/) from the original on 2023-07-14. Retrieved 2023-07-14.

1. **[^](#cite_ref-Einstein1905_9-0)** [Einstein, A.](/source/Albert_Einstein) (1905). ["Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt"](http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf) (PDF). *[Annalen der Physik](/source/Annalen_der_Physik)* (in German). **17** (6): 132–148. [Bibcode](/source/Bibcode_(identifier)):[1905AnP...322..132E](https://ui.adsabs.harvard.edu/abs/1905AnP...322..132E). [doi](/source/Doi_(identifier)):[10.1002/andp.19053220607](https://doi.org/10.1002%2Fandp.19053220607). [Archived](https://web.archive.org/web/20150924072915/http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf) (PDF) from the original on 2015-09-24. Retrieved 2010-08-26.. A partial [English translation](https://en.wikisource.org/?curid=59468) [Archived](https://web.archive.org/web/20210121022128/https://en.wikisource.org/?curid=59468) 2021-01-21 at the [Wayback Machine](/source/Wayback_Machine) is available from [Wikisource](/source/Wikisource).

1. **[^](#cite_ref-10)** Kuhn, Thomas S. (1978). [*Black-body theory and the quantum discontinuity, 1894-1912*](https://archive.org/details/blackbodytheoryq0000kuhn/mode/1up). Oxford: Clarendon Press. p. 201. [ISBN](/source/ISBN_(identifier)) [978-0-19-502383-1](https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-502383-1).

1. **[^](#cite_ref-11)** Parker, Will (2005-02-11). ["Real-World Quantum Effects Demonstrated"](http://www.scienceagogo.com/news/20050110221715data_trunc_sys.shtml). *ScienceAGoGo*. Retrieved 2023-08-20.

1. **[^](#cite_ref-12)** Modern Applied Physics-Tippens third edition; McGraw-Hill.

## Further reading

- Hoffmann, Banesh (1959). *The Strange story of the quantum: An account for the general reader of the growth of the ideas underlying our present atomic knowledge* (2 ed.). New York: Dover. [ISBN](/source/ISBN_(identifier)) [978-0-486-20518-2](https://en.wikipedia.org/wiki/Special:BookSources/978-0-486-20518-2). {{[cite book](https://en.wikipedia.org/wiki/Template:Cite_book)}}: ISBN / Date incompatibility ([help](https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_isbn_date))

- [Mehra, Jagdish](/source/Jagdish_Mehra); [Rechenberg, Helmut](/source/Helmut_Rechenberg); Mehra, Jagdish; Rechenberg, Helmut (2001). *The historical development of quantum theory. 4: Pt.1, the fundamental equations of quantum mechanics, 1925-1926* (1. softcover print ed.). New York Heidelberg: Springer. [ISBN](/source/ISBN_(identifier)) [978-0-387-95178-2](https://en.wikipedia.org/wiki/Special:BookSources/978-0-387-95178-2).

- M. Planck, *A Survey of Physical Theory*, transl. by R. Jones and D.H. Williams, Methuen & Co., Limited., London 1925 (Dover edition 17 May 2003, ISBN 978-0486678672) including the Nobel lecture.

- Rodney, Brooks (14 December 2010) *Fields of Color: The theory that escaped Einstein*. Allegra Print & Imaging. ISBN 979-8373308427

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