BoseEinstein (or BE) statistics are closely related to MaxwellBoltzmann statistics (MB) and FermiDirac statistics (FD). While FD statistics holds for fermions, MB statistics holds for "classical particles, i.e. identical but distinguishable particules, and represents the classical or hightemperature limit of both FD and BE statistics.
Bosons, unlike fermions, are not subject to the Pauli exclusion principle: an unlimited number of particles may occupy the same state at the same time. This explain why, at low temperatures, bosons can behave very differently than fermions; all the particules they will tend to congregate together at the same lowestenergy state, forming what is a BoseEinstein condensate.
BE statistics was introduced for photons in 1920 by Bose and generalized to atoms by Einstein in 1924.
The distribution function f(E) is the probability that a particle is in energy state E, for BE statistics the following hold:
where:
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