Editing Solid-state physics (section)

==Electronic properties==
Properties of materials such as [[electrical conduction]] and [[heat capacity]] are investigated by solid state physics. An early model of electrical conduction was the [[Drude model]], which applied [[kinetic theory of gases|kinetic theory]] to the [[electron]]s in a solid. By assuming that the material contains immobile positive ions and an "electron gas" of classical, non-interacting electrons, the Drude model was able to explain electrical and [[thermal conductivity]] and the [[Hall effect]] in metals, although it greatly overestimated the electronic heat capacity.

[[Arnold Sommerfeld]] combined the classical Drude model with [[quantum mechanics]] in the [[free electron model]] (or Drude-Sommerfeld model). Here, the electrons are modelled as a [[Fermi gas]], a gas of particles which obey the quantum mechanical [[Fermi–Dirac statistics]]. The free electron model gave improved predictions for the heat capacity of metals, however, it was unable to explain the existence of [[Insulator (electricity)|insulators]].

The [[nearly free electron model]] is a modification of the free electron model which includes a weak periodic [[perturbation theory (quantum mechanics)|perturbation]] meant to model the interaction between the conduction electrons and the ions in a crystalline solid. By introducing the idea of [[Electronic band structure|electronic bands]], the theory explains the existence of [[electrical conductor|conductors]], [[semiconductor]]s and [[Insulator (electricity)|insulators]].

The nearly free electron model rewrites the [[Schrödinger equation]] for the case of a periodic [[potential]]. The solutions in this case are known as [[Bloch state]]s. Since [[Bloch's theorem]] applies only to periodic potentials, and since unceasing random movements of atoms in a crystal disrupt periodicity, this use of Bloch's theorem is only an approximation, but it has proven to be a tremendously valuable approximation, without which most solid-state physics analysis would be intractable. Deviations from periodicity are treated by quantum mechanical [[perturbation theory (quantum mechanics)|perturbation theory]].