Bose–Einstein distribution

The Bose–Einstein distribution gives the mean number of bosons occupying a quantum state at a specified energy in thermal equilibrium, determined by temperature and chemical potential.

Bose–Einstein statistics: Quantum statistics governing indistinguishable bosons, which can share the same quantum state. The distribution is the thermal occupation law derived from these statistics.
Boson: A particle or quasiparticle with integer spin that obeys Bose–Einstein statistics. Only bosonic particles follow this occupation rule.
Black-body radiation: Electromagnetic radiation emitted by an ideal absorber in thermal equilibrium. Its frequency spectrum results from thermally populated photon modes.
Pauli exclusion principle: The quantum rule that no two identical fermions can occupy the same one-particle state. Its restriction distinguishes fermionic occupations from unrestricted boson sharing.
Chemical potential: A thermodynamic quantity measuring how a system's free energy changes when particles are added. It fixes the particle-number constraint in the occupation formula.
Quantum state: A mathematical description containing the information needed to predict a quantum system's measurement outcomes. The distribution assigns a mean occupation to each available state.
Bose–Einstein condensate: A state of matter in which many bosons occupy the same lowest-energy quantum state. The distribution predicts the growing ground-state population near condensation.
Classical ideal gas: A dilute gas whose particles are modeled classically, neglecting quantum statistical effects. The distribution reduces to classical gas occupations when states are sparsely populated.
Planck's law: The spectrum of thermal electromagnetic radiation, derived from Bose–Einstein occupation of photon modes. It applies the distribution to photons, whose chemical potential is zero at equilibrium.
Energy level: A permitted value of energy for a quantum system. Each state's energy enters the distribution's exponential factor.

Linked from 7 pages