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Bose–Einstein statistics
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Distribution for bosons; leads to condensation.
f(E) = 1/(e^{(E−μ)/kT}−1)Bosons (photons, helium-4) can pile into the same state: f(E) = 1/(e^{(E−μ)/kT} − 1). At low T many occupy the ground state.
Lasers rely on photon bunching.
Needs μ below the lowest energy.
In more detail
Bose-Einstein statistics describe particles with integer spin, such as photons and some atoms, which can share the same quantum state. At low temperature, many bosons can occupy the lowest state.
Real-world uses
- Laser light is produced by many photons in the same state.
- Superfluid helium follows Bose-Einstein behaviour at low temperatures.
- Photons in a laser and helium-4 atoms at low temperature follow Bose–Einstein statistics.
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Frequently asked questions
How do bosons differ from fermions?
Bosons can occupy the same state, while fermions cannot.
What examples of bosons are there?
Photons, helium-4 atoms and the Higgs boson.
What are bosons?
Particles with integer spin, such as photons and helium-4 atoms, which can share the same quantum state.
Related topics in Kinetic Theory & Statistical Physics
Partition function · Canonical ensemble · Fermi–Dirac statistics · Bose–Einstein condensate · Fermi energy · Specific heat of solids