Bose–Einstein statistics ( εi > μ)


In quantum statistics, Bose–Einstein statistics (or more colloquially B–E statistics) is one of two possible ways in which a collection of non-interacting indistinguishable particles may occupy a set of available discrete energy states, at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium.
The Bose–Einstein statistics apply only to those particles not limited to single occupancy of the same state—that is, particles that do not obey the Pauli exclusion principle restrictions. Such particles have integer values of spin and are named bosons, after the statistics that correctly describe their behaviour. There must also be no significant interaction between the particles. The expected number of particles in an energy state i for B–E statistics ( when εi > μ ) is related to the degeneracy of state, the energy of the ith state, the chemical potential and the absolute temperature.

Related formulas


njThe expected number of particles in state i, (dimensionless)
gjThe degeneracy of state i (dimensionless)
ϵjThe energy of the ith state (J)
μThe chemical potential (J)
kBoltzmann constant
TThe absolute temperature (K)