Editing Condensed matter physics (section)

===Electronic theory of solids===
{{Main|Electronic band structure}}

The metallic state has historically been an important building block for studying properties of solids.<ref name="AshcroftMermin1976"/> The first theoretical description of metals was given by [[Paul Drude]] in 1900 with the [[Drude model]], which explained electrical and thermal properties by describing a metal as an [[ideal gas]] of then-newly discovered [[electron]]s.  He was able to derive the empirical [[Wiedemann-Franz law]] and get results in close agreement with the experiments.<ref name=Hoddeson-1992/>{{rp|90–91}}  This classical model was then improved by [[Arnold Sommerfeld]] who incorporated the [[Fermi–Dirac statistics]] of electrons and was able to explain the anomalous behavior of the [[specific heat]] of metals in the [[Wiedemann–Franz law]].<ref name=Hoddeson-1992/>{{rp|101–103}}  In 1912, The structure of crystalline solids was studied by [[Max von Laue]] and Paul Knipping, when they observed the [[X-ray diffraction]] pattern of crystals, and concluded that crystals get their structure from periodic [[lattice model (physics)|lattices]] of atoms.<ref name=Hoddeson-1992/>{{rp|48}}<ref>{{cite journal|last=Eckert|first=Michael|title=Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussions|journal=Acta Crystallographica A|year=2011|volume=68|issue=1|doi=10.1107/S0108767311039985|pmid=22186281|url=http://journals.iucr.org/a/issues/2012/01/00/wx0005/index.html|bibcode= 2012AcCrA..68...30E|pages=30–39|doi-access=free}}</ref>  In 1928, Swiss physicist [[Felix Bloch]] provided a wave function solution to the [[Schrödinger equation]] with a [[Periodic function|periodic]] potential, known as [[Bloch's theorem]].<ref name=han-2010>{{cite book|last=Han|first=Jung Hoon|title=Solid State Physics|year=2010|publisher=Sung Kyun Kwan University|url=http://manybody.skku.edu/Lecture%20notes/Solid%20State%20Physics.pdf|url-status=dead|archive-url=https://web.archive.org/web/20130520224858/http://manybody.skku.edu/Lecture%20notes/Solid%20State%20Physics.pdf|archive-date=2013-05-20}}</ref>

Calculating electronic properties of metals by solving the many-body wavefunction is often computationally hard, and hence, approximation methods are needed to obtain meaningful predictions.<ref name=perdew-2010>{{cite journal|last=Perdew|first=John P.|author2=Ruzsinszky, Adrienn|author2-link=Adrienn Ruzsinszky |title=Fourteen Easy Lessons in Density Functional Theory|journal=International Journal of Quantum Chemistry|year=2010|volume=110|pages=2801–2807|url=http://www.if.pwr.wroc.pl/~scharoch/Abinitio/14lessons.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.if.pwr.wroc.pl/~scharoch/Abinitio/14lessons.pdf |archive-date=2022-10-09 |url-status=live|access-date=13 May 2012|doi=10.1002/qua.22829|issue=15|doi-access=free}}</ref> The [[Thomas–Fermi model|Thomas–Fermi theory]], developed in the 1920s, was used to estimate system energy and electronic density by treating the local electron density as a [[Variational method|variational parameter]]. Later in the 1930s, [[Douglas Hartree]], [[Vladimir Fock]] and [[John C. Slater|John Slater]] developed the so-called [[Hartree–Fock method|Hartree–Fock wavefunction]] as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted for [[Exchange symmetry|exchange statistics]] of single particle electron wavefunctions.  In general, it is very difficult to solve the Hartree–Fock equation.  Only the free electron gas case can be solved exactly.<ref name="AshcroftMermin1976">{{cite book|author1=Neil W. Ashcroft|author2=N. David Mermin|title=Solid state physics|year=1976|publisher=Saunders College|isbn=978-0-03-049346-1}}</ref>{{rp|330–337}} Finally in 1964–65, [[Walter Kohn]], [[Pierre Hohenberg]] and [[Lu Jeu Sham]] proposed the [[density functional theory]] (DFT) which gave realistic descriptions for bulk and surface properties of metals. The density functional theory has been widely used since the 1970s for band structure calculations of variety of solids.<ref name=perdew-2010 />