Editing Wannier function (section)

{{Short description|Physical function}}
[[Image:N2 Wannier.png|thumb|upright=0.85|Wannier functions of triple- and single-bonded nitrogen dimers in palladium nitride.]]
The '''Wannier functions''' are a complete set of [[orthogonal functions]] used in [[solid-state physics]]. They were introduced by [[Gregory Wannier]] in 1937.<ref name=Wannier1937>{{cite journal | doi = 10.1103/PhysRev.52.191 | volume=52 | issue=3 | title=The Structure of Electronic Excitation Levels in Insulating Crystals | year=1937 | journal=Physical Review | pages=191–197 | author=Wannier Gregory H| bibcode=1937PhRv...52..191W }}</ref><ref name=Wannier1962>{{cite journal | last=Wannier | first=Gregory H. | title=Dynamics of Band Electrons in Electric and Magnetic Fields | journal=Reviews of Modern Physics | publisher=American Physical Society (APS) | volume=34 | issue=4 | date=1 September 1962 | issn=0034-6861 | doi=10.1103/revmodphys.34.645 | pages=645–655 | bibcode=1962RvMP...34..645W}}</ref> Wannier functions are the [[localized molecular orbitals]] of crystalline systems.

The Wannier functions for different lattice sites in a [[crystal]] are orthogonal, allowing a convenient basis for the expansion of [[electron]] states in certain regimes. Wannier functions  have found widespread use, for example, in the analysis of binding forces acting on electrons.