Illustration of the Fermi-Dirac statistics

The distribution of electrons in small one-dimensional systems is obtained under the assumption of evenly spaced energy levels. The method consists of considering isolated systems and shifting electrons from their zero-temper ature location. The distribution is then expressed in terms of the number o f partitions of integers. When the system is in thermal contact with an ele ctrical insulator, the electron distribution is obtained by averaging the p revious result with the Boltzmann factor as a weight. Finally, when the sys tem is in thermal an electrical contact with a large medium, the Fermi-Dira c distribution emerges through averaging over the number N of electrons. Th e statistics of Light emitted or absorbed by the electron gas is obtained w ithout quantization of the optical field. Our rigorous though elementary tr eatment helps clarify concepts employed in statistical mechanics. (C) 1999 American Association of Physics Teachers.