Bose—Einstein Statistics

Bose-Einstein statistics is a procedure for counting the possible states of quantum systems composed of identical particles with integer ► spin. It takes its name from Satyendra Nath Bose (1894–1974), the Indian physicist who first proposed it for ► light quanta (1924), and Albert Einstein (1879–1955), who extended it to gas molecules (1924, 1925).

Both in classical and in quantum mechanics, the behaviour of systems composed of a large number of particles can be investigated with the help of statistical considerations. If all particles obey the same dynamics, and if their interactions can be neglected in a first approximation, one can determine all possible energy states of a single particle, and then make statistical assumptions on the distribution of the particles among single-particle states, thus computing the average behaviour of the whole system. The usual statistical assumption is that all possible states of the many-particle system (i.e. all configurations) are equally probable. As became clear around the middle of the 1920's, the description of quantum systems of many particles has to be different from that of classical ones, a fact usually described by referring to the ► indistinguishability of quantum particles as opposed to the distinguishability of classical ones. Two kinds of ► quantum statistics have been found to play a role in quantum mechanics: the statistics of Bose-Einstein and that of ►Fermi-Dirac.