in quantum mechanics and quantum statistics, a number that indicates the extent to which quantum states are filled by the particles of a quantum-mechanical system consisting of many identical particles. For a system consisting of fermions, or particles with half-integral spin, the occupation numbers may take only two values: 0 for empty states or 1 for filled states. For a system consisting of bosons, or particles with integral spin, the occupation numbers may take any nonnegative .integral values: 0,1, 2,. . . For a given system, the sum of all occupation numbers should be equal to the number of particles in the system.
Occupation numbers may also be used to describe the numbers of elementary excitations, or quasiparticles, of quantum fields. In this case, the sum of the occupation numbers is not fixed.
The occupation numbers averaged over a state in statistical equilibrium for ideal quantum gases are specified by either the Fermi-Dirac or the Bose-Einstein distribution function [see equation (19) in STATISTICAL MECHANICS]. The concept of occupation numbers underlies the method of second quantization, which is also called the occupation-number representation.
D. N. ZUBAREV