Illustration of the Fermi-Dirac statistics

摘要

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-temperature location. The distribution is then expressed in terms of the number of partitions of integers. When the system is in thermal contact with an electrical insulator, the electron distribution is obtained by averaging the previous result with the Boltzmann factor as a weight. Finally, when the system is in thermal an electrical contact with a large medium, the Fermi-Dirac distribution emerges through averaging over the number N of electrons. The statistics of Light emitted or absorbed by the electron gas is obtained without quantization of the optical field. Our rigorous though elementary treatment helps clarify concepts employed in statistical mechanics. (C) 1999 American Association of Physics Teachers. [References: 11]