TABLE OF CONTENTS One of the earliest successful approximations in the theory of metals was the free electron theory. This approximation starts with the notion that the metal contains a collection of ion cores, each core consisting of a nucleus and shells of tightly bound electrons, and a number of electrons that are not bound to any particular nucleus. The electrons are assumed to be essentially independent and are treated as being completely free, the metal simply acting as a box to contain them. The statistical counterpart of this assumption is that electrons in metals are described by particle statistics.
An essential parameter in free electron theory is the number of electrons per atom that are to be considered free rather than being tied up in ion cores. Usually, the number of free electrons is taken to be the number of valence electrons of the atoms. When applied to real solids, the free electron concentration can be treated as a disposable parameter to be determined by experiment, thereby providing a check on our choice of the number of free electrons per atom.
A much more basic question is involved in trying to understand how it is that the free electron theory of metals is successful at all. We know that none of the electrons in a metal can really be independent; they interact with each other and with the ion cores through strong Coulomb forces. However, there are several factors that allow the electrons to be treated as...
