In quantum physics, which statistics describe particles that can share the same quantum state?

In quantum physics, Bose–Einstein statistics describe particles that can share the same quantum state.

The statistics apply to identical bosons, particles with integer spin. Unlike fermions, bosons are not restricted by the Pauli exclusion principle, so many of them can occupy one state. Photons in a laser mode and atoms in a Bose–Einstein condensate are important examples.

Satyendra Nath Bose developed the counting method for photons in 1924, and Albert Einstein extended it to material particles. Their work predicted that a gas of bosonic atoms could undergo a transition in which a macroscopic number of atoms occupies the lowest available state at sufficiently low temperature.

Bose–Einstein statistics are not simply a synonym for all quantum behavior. Fermions follow Fermi–Dirac statistics, while classical dilute gases can often be approximated by Maxwell–Boltzmann statistics. Whether a composite particle behaves as a boson or fermion depends on its total spin, which is integer for bosons and half-integer for fermions.