# Free Electron Fermi Gas

###### 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.