Bose–Einstein statistics

Summary

Bose–Einstein statistics describes how identical bosons, such as photons or helium-4 atoms, fill the single-particle states of a system in thermal equilibrium. Any number of bosons may share one state, and the mean occupation of a state of energy $\varepsilon$ is $1/(e^{(\varepsilon - \mu)/k_B T} - 1)$. It gives Planck's law for black-body radiation, the heat capacity of crystal vibrations, and Bose–Einstein condensation. At high temperature or low density it reduces to Maxwell–Boltzmann statistics.