ABSTRACT
In nature there are two types of solids: the crystalline and the amorphous. Crystalline materials are those in which the atoms inside them are arranged periodically. The linear combination of atomic orbitals method can be extended to take into account more complicated solids that have more than one electron in their outer shell. As an electric field is applied to a solid, the electrons can be accelerated and give rise to electric current, but only if they can accept the energy of the electric field. To do so they must be in states which have empty states just above them to which they can jump as they are being accelerated. The number of electrons per unit volume n in the conduction band of a metal can be evaluated by integrating the density of states multiplied by the Fermi–Dirac probability from the bottom of the band to infinity.
