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A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac , each of whom derived the distribution independently in 1926. [ 1 ] [ 2 ] Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics .
An example of a Fermi Problem relating to total gasoline consumed by cars since the invention of cars and comparison to the output of the energy released by the sun. "Introduction to Fermi estimates" by Nuño Sempere, which has a proof sketch of why Fermi-style decompositions produce better estimates.
For comparison, the average number of fermions with energy given by Fermi–Dirac particle-energy distribution has a similar form: ¯ = / +. As mentioned above, both the Bose–Einstein distribution and the Fermi–Dirac distribution approaches the Maxwell–Boltzmann distribution in the limit of high temperature and low particle density ...
Physically, the integrals represent statistical averages using the Fermi–Dirac distribution. When the inverse temperature β {\displaystyle \beta } is a large quantity, the integral can be expanded [ 1 ] [ 2 ] in terms of β {\displaystyle \beta } as
While the Pauli principle and Fermi-Dirac distribution applies to all matter, the interesting cases for degenerate matter involve systems of many fermions. These cases can be understood with the help of the Fermi gas model. Examples include electrons in metals and in white dwarf stars and neutrons in neutron stars.
For example, in a piece of aluminum there are two conduction bands crossing the Fermi level (even more bands in other materials); [10] each band has a different edge energy, ϵ C, and a different ζ. The value of ζ at zero temperature is widely known as the Fermi energy , sometimes written ζ 0 .
Fermi-von Neumann elephant In recreational mathematics , von Neumann's elephant is a problem consisting of constructing a planar curve in the shape of an elephant from only four fixed parameters. It originated from a discussion between physicists John von Neumann and Enrico Fermi .
When a semiconductor is in thermal equilibrium, the distribution function of the electrons at the energy level of E is presented by a Fermi–Dirac distribution function. In this case the Fermi level is defined as the level in which the probability of occupation of electron at that energy is 1 ⁄ 2. In thermal equilibrium, there is no need to ...