Quantum

In physics, a quantum (pl.: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization".[1] This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an 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. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing nature.

## Contents

* 1 Origin
* 2 Quantization
* 3 See also
* 4 References
* 5 Further reading

## Origin

German physicist and 1918 Nobel Prize for Physics recipient Max Planck (1858–1947)

The modern concept of the quantum in physics originates from December 14, 1900, when Max Planck reported his findings to the German Physical Society. He showed that modelling harmonic oscillators with discrete energy levels resolved a longstanding problem in the theory of 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. 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,[6] Planck introduced the constant h, which he termed the "quantum of action" (elementares Wirkungsquantum) in 1906.[5] In this paper, Planck also reported more precise values for the elementary charge and the Avogadro-Loschmidt number, the number of molecules in one mole of substance.[7] The constant h is now known as the Planck constant. After his theory was validated, Planck was awarded the Nobel Prize in Physics for his discovery in 1918.[8]

In 1905 Albert Einstein suggested that electromagnetic radiation exists in spatially localized packets which he called "quanta of light" (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's experiments on the photoelectric effect.[3]: 23 Shortly thereafter, the term "energy quantum" was introduced for the quantity hν.[10]

## Quantization

While quantization was first discovered in 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
* History of quantum mechanics
* Quantum geometry

## References

1. ↑ Wiener, N. (1966). Differential Space, Quantum Systems, and Prediction. Cambridge, Massachusetts: The Massachusetts Institute of Technology Press
2. ↑ Rovelli, Carlo (January 2017). Reality is not what it seems: the elementary structure of things (1st American ed.). New York, New York: Riverhead Books. pp. 109–130. ISBN 978-0-7352-1392-0.
3. ↑ 3.0 3.1 Baggott, J. E. (2013). The quantum story: a history in 40 moments (Pbk ed.). Oxford [England]: Oxford University Press. ISBN 978-0-19-965597-7.
4. ↑ Planck, M. (1901). "Ueber die Elementarquanta der Materie und der Elektricität" (in de). Annalen der Physik 309 (3): 564–566. doi:10.1002/andp.19013090311. Bibcode: 1901AnP...309..564P. https://zenodo.org/record/1423997. Retrieved 2019-09-16.
5. ↑ 5.0 5.1 5.2 Quantum (3rd ed.), Oxford University Press, 2007, http://www.oed.com/view/Entry/1164299139, retrieved 6 May 2025 (Subscription or UK public library membership required.)
6. ↑ Planck, Max (1901), "Ueber das Gesetz der Energieverteilung im Normalspectrum" (in de), Annalen der Physik 309 (3): 553–63, doi:10.1002/andp.19013090310, Bibcode: 1901AnP...309..553P, http://www.physik.uni-augsburg.de/annalen/history/historic-papers/1901_309_553-563.pdf, retrieved 2008-12-15 . English translations:
* "On the Law of Distribution of Energy in the Normal Spectrum". http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html.
* "On the Law of Distribution of Energy in the Normal Spectrum". http://theochem.kuchem.kyoto-u.ac.jp/Ando/planck1901.pdf.
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:10.1007/BF00327765.
8. ↑ "Max Planck Nobel Lecture". https://www.nobelprize.org/prizes/physics/1918/planck/lecture/.
9. ↑ Einstein, A. (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" (in de). Annalen der Physik 17 (6): 132–148. doi:10.1002/andp.19053220607. Bibcode: 1905AnP...322..132E. http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf. Retrieved 2010-08-26. . A partial English translation is available from Wikisource.
10. ↑ Kuhn, Thomas S. (1978). Black-body theory and the quantum discontinuity, 1894-1912. Oxford: Clarendon Press. pp. 201. ISBN 978-0-19-502383-1. https://archive.org/details/blackbodytheoryq0000kuhn/mode/1up.
11. ↑ Parker, Will (2005-02-11). "Real-World Quantum Effects Demonstrated" (in en-US). http://www.scienceagogo.com/news/20050110221715data_trunc_sys.shtml.
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 978-0-486-20518-2.
* Mehra, Jagdish; Rechenberg, Helmut; 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 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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Quantum mechanics

Background|

* Introduction
* History
* timeline
* Glossary
* Classical mechanics
* Old quantum theory

Fundamentals|

* Bra–ket notation
* Casimir effect
* Complementarity
* Density matrix
* Energy level
* ground state
* excited state
* degenerate levels
* Vacuum state
* Zero-point energy
* QED vacuum
* QCD vacuum
* Hamiltonian
* Operator
* Quantum coherence
* Quantum decoherence
* Measurement
* Quantum
* Quantum realm
* Quantum system
* Quantum state
* Quantum number
* Quantum entanglement
* Quantum superposition
* Quantum nonlocality
* Quantum tunnelling
* Quantum levitation
* Quantum fluctuation
* Quantum annealing
* Quantum foam
* Quantum noise
* Heisenberg uncertainty principle
* Spontaneous parametric down-conversion
* Von Neumann entropy
* Spin
* Scattering theory
* Symmetry in quantum mechanics
* Symmetry breaking
* Spontaneous symmetry breaking
* Wave propagation
* Quantum interference
* Wave function
* Wave function collapse
* Wave–particle duality
* Matter wave
* Qubit
* Qutrit
* Observable
* Probability distribution

Formulations|

* Formulations
* Heisenberg
* Interaction
* Matrix mechanics
* Schrödinger
* Path integral formulation
* Phase space

Equations|

* Dirac
* Klein–Gordon
* Pauli
* Rydberg
* Schrödinger

Interpretations|

* Interpretations
* Bayesian
* Consistent histories
* Copenhagen
* de Broglie–Bohm
* Ensemble
* Hidden variables
* Many worlds
* Objective collapse
* Quantum logic
* Relational
* Stochastic
* Transactional
* Cosmological

Experiments|

* Afshar
* Bell's inequality
* Cold Atom Laboratory
* Davisson–Germer
* Delayed-choice quantum eraser
* Double-slit
* Franck–Hertz experiment
* Leggett–Garg inequality
* Mach-Zehnder inter.
* Elitzur–Vaidman
* Popper
* Quantum eraser
* Schrödinger's cat
* Quantum suicide and immortality
* Stern–Gerlach
* Wheeler's delayed choice

Science|

* Q-analog
* List
* Quantum algebra
* Quantum calculus
* Quantum differential calculus
* Quantum geometry
* Quantum group
* Quantum Bayesianism
* Quantum biology
* Quantum chemistry
* Quantum chaos
* Quantum cognition
* Quantum cosmology
* Quantum dynamics
* Quantum economics
* Quantum evolution
* Quantum finance
* Quantum game theory
* Quantum measurement problem
* Quantum mind
* Quantum probability
* Quantum social science
* Quantum stochastic calculus
* Quantum spacetime

Technology|

* Quantum algorithms
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* Quantum cellular automata
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* Quantum electronics
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* Phase qubit
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* Quantum dot
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* Timeline
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* Quantum error correction
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* Quantum metrology
* Quantum network
* Quantum neural network
* Quantum optics
* Quantum programming
* Quantum sensors
* Quantum simulator
* Quantum teleportation
* Quantum levitation
* Time travel
* Quantum complexity theory

Extensions|

* Quantum statistical mechanics
* Relativistic quantum mechanics
* Quantum field theory
* Axiomatic quantum field theory
* Quantum field theory in curved spacetime
* Thermal quantum field theory
* Topological quantum field theory
* Local quantum field theory
* Conformal field theory
* Two-dimensional conformal field theory
* Liouville field theory
* History
* Quantum gravity

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