What name is given to the quantum rule that identical bosons can occupy one shared state?

Bose–Einstein statistics is the quantum rule describing identical bosons that can occupy one shared state.

Bosons have integer-valued spin, such as 0, 1, or 2, and their quantum state is unchanged when two identical particles are exchanged. Unlike fermions, they are not restricted by the Pauli exclusion principle. Any number of bosons can therefore occupy the same single-particle state.

Satyendra Nath Bose developed the statistical treatment of photons in 1924, and Albert Einstein extended it in 1924 and 1925 to material particles. The theory predicted that a dilute gas of bosons could undergo Bose–Einstein condensation at sufficiently low temperature.

Bose–Einstein statistics is not the same as the Bose–Einstein condensate. The first term is the counting rule; the second is a collective state of matter produced under suitable conditions. Photons, gluons, and helium-4 atoms are examples of bosonic systems, although their physical settings differ greatly.