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A Fermi gas is an idealized model, ... Density of states (DOS) of a Fermi gas in 3-dimensions. For the 3D uniform Fermi gas, with fermions of spin- ...
The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
A result is the Fermi–Dirac distribution of particles over these states where no two particles can occupy the same state, which has a considerable effect on the properties of the system. Fermi–Dirac statistics is most commonly applied to electrons , a type of fermion with spin 1/2 .
Using the results from either Maxwell–Boltzmann statistics, Bose–Einstein statistics or Fermi–Dirac statistics we use the Thomas–Fermi approximation (gas in a box) and go to the limit of a very large trap, and express the degeneracy of the energy states as a differential, and summations over states as integrals.
Under the free electron model, the electrons in a metal can be considered to form a Fermi gas.The number density / of conduction electrons in metals ranges between approximately 10 28 and 10 29 electrons/m 3, which is also the typical density of atoms in ordinary solid matter.
The term also applies to metals in the Fermi gas approximation. Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble of non-interacting fermions. In a quantum mechanical description, particles limited to a finite volume may take only a discrete set of energies, called quantum states.
Insulators have zero density of states at the Fermi level due to their band gaps. Thus, the density of states-based electronic entropy is essentially zero in these systems. Metals have non-zero density of states at the Fermi level. Metals with free-electron-like band structures (e.g. alkali metals, alkaline earth metals, Cu, and Al) generally ...
Fig. 1: Fermi surface and electron momentum density of copper in the reduced zone schema measured with 2D ACAR. [6]Consider a spin-less ideal Fermi gas of particles. . According to Fermi–Dirac statistics, the mean occupation number of a state with energy is give