Physics:Quantum Bose–Einstein statistics: Difference between revisions

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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}}

Revision as of 22:03, 23 May 2026

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Bose–Einstein statistics describe the occupation of quantum states by identical bosons. They apply to particles with integer spin, including photons, gluons, phonons, and many composite particles.

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Bose-Einstein statistics allow many bosons to occupy the same quantum state.

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 E is

n(E)=1exp⁡((E−μ)/kBT)−1

where μ is the chemical potential, kB is the Boltzmann constant, and T 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 Bose-Einstein condensate.

Historical names

See also

Table of contents (84 articles)

Index

Full contents

References

  • Annett, James F. (2004). Superconductivity, Superfluids and Condensates. New York: Oxford University Press. ISBN 0-19-850755-0. 
  • McQuarrie, Donald A. (2000). Statistical Mechanics (1st ed.). Sausalito, CA: University Science Books. ISBN 1-891389-15-7. 
  • Ziff, R. M.; Kac, M.; Uhlenbeck, G. E. (1977). "The ideal Bose-Einstein gas, revisited". Physics Reports 32: 169-248. 


Author: Harold Foppele


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