Physics:Quantum Bose–Einstein statistics

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

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.

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

$n(E)=\frac{1}{\exp ((E-\mu )/k_{\mathrm{B}}T)-1}$

where $\mu$ is the chemical potential, $k_{\mathrm{B}}$ 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

• Satyendra Nath Bose derived the counting rule for photons.
• Albert Einstein extended Bose's idea to material particles.

Related concepts

• Physics:Quantum boson
• Physics:Quantum photon
• Physics:Quantum Fermi–Dirac statistics

References

• Bose, S. N. (1924). "Plancks Gesetz und Lichtquantenhypothese". Zeitschrift für Physik 26: 178-181. doi:10.1007/BF01327326. 
• "Bose-Einstein statistics". https://www.britannica.com/science/Bose-Einstein-statistics. 

Author: Harold Foppele