Quantum statistics

Quantum statistics describes how indistinguishable particles occupy available quantum states. Its two main forms, Bose–Einstein and Fermi–Dirac statistics, follow from different exchange symmetries of particle states.

Bose–Einstein statistics: The quantum statistics governing identical bosons, which may share the same quantum state. Symmetric exchange states allow bosons to accumulate in one state.
Quantum state: A mathematical description containing the information available about a quantum system. Statistics count how many particles can occupy each possible state.
Black-body radiation: Thermal electromagnetic radiation whose spectrum depends on the temperature of an ideal absorber and emitter. Planck's spectrum follows from applying Bose–Einstein statistics to photon modes.
Bose–Einstein distribution: The equilibrium mean occupation of a bosonic state as a function of energy, temperature, and chemical potential. It quantifies the state populations allowed by bosonic statistics.
Satyendra Nath Bose: An Indian physicist whose 1924 derivation of photon statistics helped establish Bose–Einstein statistics. His state-counting method supplied the basis for the bosonic distribution.
Fermi–Dirac statistics: The quantum statistics governing identical fermions, which obey the Pauli exclusion principle. Antisymmetric exchange states prevent identical fermions from sharing a state.
Identical particles: Particles of the same species that share intrinsic properties and cannot be individually distinguished in quantum mechanics. Their indistinguishability makes exchange symmetry physically significant.
Bose–Einstein condensation: A phase in which a macroscopic number of bosons occupy the lowest available quantum state. It is a striking consequence of bosonic state sharing at low temperature.
Fermi–Dirac distribution: The equilibrium mean occupation of a fermionic state as a function of energy, temperature, and chemical potential. It shows how exclusion limits each fermionic state to one particle.
Albert Einstein: A German-born theoretical physicist who extended Bose's photon statistics to material particles. His extension predicted the condensation of a gas of identical bosons.

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