CHAPTER V - THE FERMI AND BOSE DISTRIBUTIONS

Abstract

This chapter discusses the Fermi and Bose distributions. If the temperature of an ideal gas is low, Boltzmann statistics becomes inapplicable and a different statistics must be devised in which the mean occupation numbers of the various quantum states of particles are not assumed small. This statistics differs according to the type of wave functions by which the gas is described when regarded as a system of N identical particles. These functions must be either anti-symmetrical or symmetrical with respect to interchanges of any pair of particles, the former case occurring for particles with half-integral spin, and the latter case for those with integral spin. For a system of particles described by anti-symmetrical wave functions, Pauli's principle applies, that is, in each quantum state there cannot simultaneously be more than one particle. The statistics based on this principle is called Fermi statistics or Fermi-Dirac statistics. By contrast, in Bose statistics, the value of the gas pressure changes in the opposite direction, becoming less than the classical value, which means there is an effective attraction between the particles.