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Free Electron Fermi Gas

November 19, 2008
From C. Kittel’s Introduction to Solid State Physics, 4th ed. Wiley (1971)

A conduction electron in a metal can move freely in a straight path over many atomic distances.
Why condensed matter is so transparent to conduction electrons?

(a) A conduction electron is not deflected by ion cores arranged on a periodic lattice because matter wave propagate freely in a periodic structure.
(b) A conduction electron is scattered only infrequently by other conduction electron as a consequence of the Pauli exclusion principle.

By a free electron Fermi gas we shall mean a gas of free and non- interacting electrons which are subject to the Pauli principle.

We use the term orbital to denote a solution of the wave equation for a system of only one electron. The term allows us to distinguish between an exact quantum state of the wave equation of a system of N electrons and an approximate quantum state which we construct by assigning the N electrons to N different orbitals, where each orbital is a solution of a wave equation for one electron.

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