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 Wannierequation describes a quantum mechanical eigenvalue problem in solids where an electron in a conduction band and an electronic vacancy (i.e...
Gregory Hugh Wannier (1911–1983) was a Swiss physicist. He developed a complete set of orthogonal functions known as the Wannier functions which became...
this approach. For these reasons, it is more convenient to use the set of Wannier functions. Applying an electric field F to the superlattice structure causes...
ISBN 978-0-471-75687-3. Longhi, Stefano; Janner, Davide (2008). "Localization and Wannier wave packets in photonic crystals". In Hugo E. Hernández-Figueroa; Michel...
defined by the generalized Wannierequation not the free-carrier energies. For low electron–hole densities, the Wannierequation produces a set of bound...
through the generalized Wannierequation that can be solved analytically in special cases. In particular, the low-density Wannierequation is analogous to bound...
{(R_{n},r)} }} are called Wannier functions, and are fairly closely localized to the atomic site Rn. Of course, if we have exact Wannier functions, the exact...
Wannierequation. The many-body Coulomb interaction leads to significant complications since it results in an infinite hierarchy of dynamic equations...
{\displaystyle {\tilde {F}}({\bf {R}})} is a measure of the overlap of Wannier functions centered at two home cells that are distance R {\displaystyle...
solutions based upon the crystal potential. Wannier functions on different atomic sites R are orthogonal. The Wannier functions can be used to form the Schrödinger...
the Kramers–Kronig relations with Ralph Kronig which are mathematical equations relating real and imaginary parts of complex functions constrained by...
description of quantum mechanics, with an emphasis on the Schrödinger equation in real space. The second describes atomic and electronic collisions in...
of states Electron and spin density Bader charges and critical points Wannier functions Total energies and energy differences Fermi surfaces Optical...
sectors, separated domains not linked by finite fluctuations. Kramers and Wannier were able to show that the high-temperature expansion and the low-temperature...
first based on a semiclassical approach, then on a derivation from the Wannier representation, and finally from a long-wavelength expansion. The resulting...
the laser itself. The amplification of coherent terahertz sound in a Wannier–Stark ladder superlattice has been achieved in 2009 according to a paper...
unit cells, and the ϕ R {\displaystyle \phi _{\mathbf {R} }} are known as Wannier functions. The corresponding eigenvalues E ( k ) {\displaystyle E\left(\mathbf...
delocalized, symmetry adapted molecular orbitals used in molecules (while Wannier functions correspond to localized molecular orbitals). A number of important...
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