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Under the free electron model, the electrons in a metal can be considered to form a uniform Fermi gas. The number density N / V {\displaystyle N/V} of conduction electrons in metals ranges between approximately 10 28 and 10 29 electrons per m 3 , which is also the typical density of atoms in ordinary solid matter.
In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, [1] principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
Under the free electron model, the electrons in a metal can be considered to form a Fermi gas. The number density N / V {\displaystyle N/V} 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.
Friedel oscillations of the electron density in 1D electron gas occupying the half-space >.Here, = /, and is the Fermi wave vector. As a simple model, consider one-dimensional electron gas in a half-space >.
Since metals can display multiple oxidation numbers, the exact definition of how many "valence electrons" an element should have in elemental form is somewhat arbitrary, but the following table lists the free electron densities given in Ashcroft and Mermin, which were calculated using the formula above based on reasonable assumptions about ...
Luttinger liquid theory describes low energy excitations in a 1D electron gas as bosons. Starting with the free electron Hamiltonian: = † is separated into left and right moving electrons and undergoes linearization with the approximation () over the range :
This expression is sometimes called "the Mott formula", however it is much less general than Mott's original formula expressed above. In the free electron model with scattering, the value of ′ / is of order / (), where is the Fermi temperature, and so a typical value of the Seebeck coefficient in the Fermi gas is / (the prefactor varies ...
For electrons or electron holes in a solid, the effective mass is usually stated as a factor multiplying the rest mass of an electron, m e (9.11 × 10 −31 kg). This factor is usually in the range 0.01 to 10, but can be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials , or anywhere from zero to infinity ...