1938/02/07 by Jane McDougall, Edmund C. Stoner · 442 citations
Physics and Astronomy · Mathematics · #Statistical Mechanics and Entropy #Advanced Thermodynamics and Statistical Mechanics #Scientific Research and Discoveries #Fermi–Dirac statistics #Physics #Range (aeronautics) #Energy (signal processing) #Statistics #Fermi energy #Basis (linear algebra) #Computation #Mathematical physics #Fermi Gamma-ray Space Telescope #Statistical physics #Quantum mechanics #Mathematics #Electron #Geometry
paper · doi:10.1098/rsta.1938.0004
published in Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences 237(773), 67-104 (Royal Society)
openalex publication_date 1938/02/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/26
Abstract The quantitative application of Fermi-Dirac statistics involves the evaluation of certain integrals which have not previously been tabulated. In this paper, tables are given of the values of the basic integrals most frequently required , with a view to placing Fermi-Dirrac statistics on as firm a numerical basis as is Maxwell-Boltzmann statistics. T e expression for the energy distribution of particles subject to Fermi-Dirrac statistics may be written in the form dN He) de e<*+Pe -)-1 ’ wherev(e) is the number of states per unit energy range, and dN is the number of particles in the energy range e to e--de. In the statistical treatment, the parameters ot and fi, which are usually introduced as undetermined multipliers in a variational equation, are to be determined from two equations expressing conditions imposed by the total number of particles, and the total energy of the system. By linking up the statistical and thermodynamical treatments, interpretation can be given to a and b this is expressed by P**:l IkT, a = -C lk T ,