Physics:Quantum Bose–Einstein statistics - Revision history

WikiHarold: Expand short Quantum intro

2026-05-23T22:58:47Z

Expand short Quantum intro

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	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	'''Bose–Einstein statistics''' describe the occupation of quantum states by identical [[Physics:Quantum boson\|bosons]]. They apply to particles with integer spin, including [[Physics:Quantum photon\|photons]], gluons, phonons, and many composite particles.<ref>{{Cite book \|last=Annett \|first=James F. \|title=Superconductivity, Superfluids and Condensates \|location=New York \|publisher=Oxford University Press \|year=2004 \|isbn=0-19-850755-0}}</ref>		'''Bose–Einstein statistics''' is a Book II topic in the Quantum Collection. '''Bose–Einstein statistics''' describe the occupation of quantum states by identical [[Physics:Quantum boson\|bosons]]. They apply to particles with integer spin, including [[Physics:Quantum photon\|photons]], gluons, phonons, and many composite particles.<ref>{{Cite book \|last=Annett \|first=James F. \|title=Superconductivity, Superfluids and Condensates \|location=New York \|publisher=Oxford University Press \|year=2004 \|isbn=0-19-850755-0}}</ref> Bose-Einstein statistics allow many identical bosons to occupy the same quantum state, which makes collective quantum behavior possible. They explain blackbody radiation, photon bunching, superfluidity, and Bose-Einstein condensation. The statistics arise from symmetric many-particle wavefunctions and contrast sharply with the exclusion behavior of fermions.
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WikiHarold: Move Quantum references inline

2026-05-23T22:15:11Z

Move Quantum references inline

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	'''Bose–Einstein statistics''' describe the occupation of quantum states by identical [[Physics:Quantum boson\|bosons]]. They apply to particles with integer spin, including [[Physics:Quantum photon\|photons]], gluons, phonons, and many composite particles.		'''Bose–Einstein statistics''' describe the occupation of quantum states by identical [[Physics:Quantum boson\|bosons]]. They apply to particles with integer spin, including [[Physics:Quantum photon\|photons]], gluons, phonons, and many composite particles.<ref>{{Cite book \|last=Annett \|first=James F. \|title=Superconductivity, Superfluids and Condensates \|location=New York \|publisher=Oxford University Press \|year=2004 \|isbn=0-19-850755-0}}</ref>
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	== Physical meaning ==		== Physical meaning ==
	Bose-Einstein statistics explain blackbody radiation, collective excitations such as phonons, and the possibility of macroscopic occupation of a single quantum state. At low temperature, some bosonic systems can form a Bose-Einstein condensate.		Bose-Einstein statistics explain blackbody radiation, collective excitations such as phonons, and the possibility of macroscopic occupation of a single quantum state. At low temperature, some bosonic systems can form a Bose-Einstein condensate.<ref>{{Cite journal \|last=Ziff \|first=R. M. \|last2=Kac \|first2=M. \|last3=Uhlenbeck \|first3=G. E. \|title=The ideal Bose-Einstein gas, revisited \|journal=Physics Reports \|year=1977 \|volume=32 \|pages=169-248}}</ref>

	== Historical names ==		== Historical names ==
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	== References ==		== References ==
	{{reflist\|3}}		{{reflist\|3}}
	* {{Cite book \|last=Annett \|first=James F. \|title=Superconductivity, Superfluids and Condensates \|location=New York \|publisher=Oxford University Press \|year=2004 \|isbn=0-19-850755-0}}
	* {{Cite book \|last=McQuarrie \|first=Donald A. \|title=Statistical Mechanics \|edition=1st \|location=Sausalito, CA \|publisher=University Science Books \|year=2000 \|isbn=1-891389-15-7}}
	* {{Cite journal \|last=Ziff \|first=R. M. \|last2=Kac \|first2=M. \|last3=Uhlenbeck \|first3=G. E. \|title=The ideal Bose-Einstein gas, revisited \|journal=Physics Reports \|year=1977 \|volume=32 \|pages=169-248}}

	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

WikiHarold: Replace Quantum references with Wikipedia-sourced references

2026-05-23T22:03:00Z

Replace Quantum references with Wikipedia-sourced references

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	== References ==		== References ==
	{{reflist\|3}}		{{reflist\|3}}
	* {{Cite ~~journal~~ \|last=~~Bose~~ \|first=~~S. N~~. \|title=~~Plancks Gesetz und Lichtquantenhypothese~~ \|~~journal~~=~~Zeitschrift für Physik~~ \|year=~~1924~~ \|~~volume~~=26 \|~~pages~~=~~178-181~~ \|~~doi~~=10.~~1007/BF01327326~~}}		* {{Cite book \|last=Annett \|first=James F. \|title=Superconductivity, Superfluids and Condensates \|location=New York \|publisher=Oxford University Press \|year=2004 \|isbn=0-19-850755-0}}
	* {{Cite ~~web~~ \|~~title~~=~~Bose-Einstein statistics~~ \|~~url~~=~~https://www~~.~~britannica~~.~~com/science/~~Bose-Einstein~~-statistics~~ \|~~website~~=~~Encyclopaedia Britannica~~ \|~~access-date~~=~~2026-05~~-23}}		* {{Cite book \|last=McQuarrie \|first=Donald A. \|title=Statistical Mechanics \|edition=1st \|location=Sausalito, CA \|publisher=University Science Books \|year=2000 \|isbn=1-891389-15-7}}
			* {{Cite journal \|last=Ziff \|first=R. M. \|last2=Kac \|first2=M. \|last3=Uhlenbeck \|first3=G. E. \|title=The ideal Bose-Einstein gas, revisited \|journal=Physics Reports \|year=1977 \|volume=32 \|pages=169-248}}

	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

WikiHarold: Use Quantum See also index module

2026-05-23T21:57:42Z

Use Quantum See also index module

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	== See also ==		== See also ==
	* [[Physics:~~Quantum boson]]~~		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also/Matter}}
	* [[Physics:Quantum photon]]
	* [[Physics:Quantum ~~Fermi–Dirac statistics]]~~

	== References ==		== References ==

WikiHarold: Remove leading BOM from Quantum page

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	{{Short description\|Quantum statistics for bosons}}		{{Short description\|Quantum statistics for bosons}}
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	{{Quantum article nav\|previous=Physics:Quantum Fermi–Dirac statistics\|previous label=Fermi-Dirac statistics\|next=Physics:Quantum boson\|next label=Boson}}		{{Quantum article nav\|previous=Physics:Quantum Fermi–Dirac statistics\|previous label=Fermi-Dirac statistics\|next=Physics:Quantum boson\|next label=Boson}}

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	{{Short description\|Quantum statistics for bosons}}		{{Short description\|Quantum statistics for bosons}}
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	{{Quantum article nav\|previous=Physics:Quantum Fermi–Dirac statistics\|previous label=Fermi-Dirac statistics\|next=Physics:Quantum boson\|next label=Boson}}		{{Quantum article nav\|previous=Physics:Quantum Fermi–Dirac statistics\|previous label=Fermi-Dirac statistics\|next=Physics:Quantum boson\|next label=Boson}}
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	* [[Biography:Albert Einstein\|Albert Einstein]] extended Bose's idea to material particles.		* [[Biography:Albert Einstein\|Albert Einstein]] extended Bose's idea to material particles.

	== ~~Related concepts~~ ==		== See also ==
	* [[Physics:Quantum boson]]		* [[Physics:Quantum boson]]
	* [[Physics:Quantum photon]]		* [[Physics:Quantum photon]]

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2026-05-23T21:41:41Z

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	{{Quantum article nav\|previous=Physics:Quantum Fermi–Dirac statistics\|previous label=Fermi-Dirac statistics\|next=Physics:Quantum boson\|next label=Boson}}		{{Quantum article nav\|previous=Physics:Quantum Fermi–Dirac statistics\|previous label=Fermi-Dirac statistics\|next=Physics:Quantum boson\|next label=Boson}}

	~~[[File~~:~~Quantum_Bose_Einstein_statistics_educational_yellow.png\|thumb\|right\|Bose~~-~~Einstein statistics allow many bosons to occupy the same quantum state.]]~~		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

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	'''Bose–Einstein statistics''' describe the occupation of quantum states by identical [[Physics:Quantum boson\|bosons]]. They apply to particles with integer spin, including [[Physics:Quantum photon\|photons]], gluons, phonons, and many composite particles.		'''Bose–Einstein statistics''' describe the occupation of quantum states by identical [[Physics:Quantum boson\|bosons]]. They apply to particles with integer spin, including [[Physics:Quantum photon\|photons]], gluons, phonons, and many composite particles.
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			[[File:Quantum_Bose_Einstein_statistics_educational_yellow.png\|thumb\|280px\|Bose-Einstein statistics allow many bosons to occupy the same quantum state.]]
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	== Description ==		== Description ==

Maintenance script: Remove red link from Bose-Einstein statistics page

2026-05-23T10:08:29Z

Remove red link from Bose-Einstein statistics page

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	{{Short description\|Quantum statistics for bosons}}		{{Short description\|Quantum statistics for bosons}}
	{{Quantum matter backlink\|Atoms}}		{{Quantum matter backlink\|Atoms}}
	{{Quantum article nav\|previous=Physics:Quantum Fermi–Dirac statistics\|previous label=Fermi-Dirac statistics\|next=Physics:Quantum ~~Bose-Einstein condensate~~\|next label=~~Bose-Einstein condensate~~}}		{{Quantum article nav\|previous=Physics:Quantum Fermi–Dirac statistics\|previous label=Fermi-Dirac statistics\|next=Physics:Quantum boson\|next label=Boson}}

	[[File:Quantum_Bose_Einstein_statistics_educational_yellow.png\|thumb\|right\|Bose-Einstein statistics allow many bosons to occupy the same quantum state.]]		[[File:Quantum_Bose_Einstein_statistics_educational_yellow.png\|thumb\|right\|Bose-Einstein statistics allow many bosons to occupy the same quantum state.]]
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	== Physical meaning ==		== Physical meaning ==
	Bose-Einstein statistics explain blackbody radiation, collective excitations such as phonons, and the possibility of macroscopic occupation of a single quantum state. At low temperature, some bosonic systems can form a ~~[[Physics:Quantum~~ Bose-Einstein condensate~~\|Bose-Einstein condensate]]~~.		Bose-Einstein statistics explain blackbody radiation, collective excitations such as phonons, and the possibility of macroscopic occupation of a single quantum state. At low temperature, some bosonic systems can form a Bose-Einstein condensate.

	== Historical names ==		== Historical names ==
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	* [[Physics:Quantum photon]]		* [[Physics:Quantum photon]]
	* [[Physics:Quantum Fermi–Dirac statistics]]		* [[Physics:Quantum Fermi–Dirac statistics]]
	* [[Physics:Quantum Bose-Einstein condensate]]

	== References ==		== References ==

Maintenance script: Create Bose-Einstein statistics page

2026-05-23T10:05:32Z

Create Bose-Einstein statistics page

New page

{{Short description|Quantum statistics for bosons}}
{{Quantum matter backlink|Atoms}}
{{Quantum article nav|previous=Physics:Quantum Fermi–Dirac statistics|previous label=Fermi-Dirac statistics|next=Physics:Quantum Bose-Einstein condensate|next label=Bose-Einstein condensate}}

[[File:Quantum_Bose_Einstein_statistics_educational_yellow.png|thumb|right|Bose-Einstein statistics allow many bosons to occupy the same quantum state.]]

'''Bose–Einstein statistics''' describe the occupation of quantum states by identical [[Physics:Quantum boson|bosons]]. They apply to particles with integer spin, including [[Physics:Quantum photon|photons]], gluons, phonons, and many composite particles.

== Description ==
Unlike fermions, bosons are not restricted by the Pauli exclusion principle. Many identical bosons can occupy the same quantum state. For a system in thermal equilibrium, the average occupation of a state with energy <math>E</math> is

<math>n(E)=\frac{1}{\exp\left((E-\mu)/k_{\mathrm B}T\right)-1}</math>

where <math>\mu</math> is the chemical potential, <math>k_{\mathrm B}</math> is the Boltzmann constant, and <math>T</math> is temperature.

== Physical meaning ==
Bose-Einstein statistics explain blackbody radiation, collective excitations such as phonons, and the possibility of macroscopic occupation of a single quantum state. At low temperature, some bosonic systems can form a [[Physics:Quantum Bose-Einstein condensate|Bose-Einstein condensate]].

== Historical names ==
* [[Biography:Satyendra Nath Bose|Satyendra Nath Bose]] derived the counting rule for photons.
* [[Biography:Albert Einstein|Albert Einstein]] extended Bose's idea to material particles.

== Related concepts ==
* [[Physics:Quantum boson]]
* [[Physics:Quantum photon]]
* [[Physics:Quantum Fermi–Dirac statistics]]
* [[Physics:Quantum Bose-Einstein condensate]]

== References ==
{{reflist|3}}
* {{Cite journal |last=Bose |first=S. N. |title=Plancks Gesetz und Lichtquantenhypothese |journal=Zeitschrift für Physik |year=1924 |volume=26 |pages=178-181 |doi=10.1007/BF01327326}}
* {{Cite web |title=Bose-Einstein statistics |url=https://www.britannica.com/science/Bose-Einstein-statistics |website=Encyclopaedia Britannica |access-date=2026-05-23}}

{{Author|Harold Foppele}}