Wannier equation

rdf:langString Wannier equation

rdf:langString The Wannier equation describes a quantum mechanical eigenvalue problem in solids where an electron in a conduction band and an electronic vacancy (i.e. hole) within a valence band attract each other via the Coulomb interaction. For one electron and one hole, this problem is analogous to the Schrödinger equation of the hydrogen atom; and the bound-state solutions are called excitons. When an exciton's radius extends over several unit cells, it is referred to as a Wannier exciton in contrast to Frenkel excitons whose size is comparable with the unit cell. An excited solid typically contains many electrons and holes; this modifies the Wannier equation considerably. The resulting generalized Wannier equation can be determined from the homogeneous part of the semiconductor Bloch equations or the semiconductor luminescence equations. The equation is named after Gregory Wannier.