The Wannier functions are a complete set of orthogonal functions used in solid-state physics. They were introduced by Gregory Wannier in 1937. Wannier functions...

isolated atoms, the Wannier function would become an isolated atomic orbital. That limit suggests the choice of an atomic wave function as an approximate...

Gregory Hugh Wannier (1911–1983) was a Swiss physicist. He developed a complete set of orthogonal functions known as the Wannier functions which became...

Cu-Pt type ordering in III-V semiconductor Tube-based nanostructures Wannier function Johansson; Linde (1925). "The X-ray determination of the atomic arrangement...

based upon the crystal potential. Wannier functions on different atomic sites R are orthogonal. The Wannier functions can be used to form the Schrödinger...

eigenvectors Hilbert space Karhunen–Loève theorem Lauricella's theorem Wannier function Antoni Zygmund (1935) Trigonometrical Series, page 6, Mathematical...

boundary conditions Symmetries in quantum mechanics Tight-binding model Wannier function Bloch, F. (1929). Über die quantenmechanik der elektronen in kristallgittern...

The Kramers–Wannier duality is a symmetry in statistical physics. It relates the free energy of a two-dimensional square-lattice Ising model at a low...

equation is obeyed in the (time-dependent) Wannier function basis. The terms come from the Wannier functions' time dependence. Otherwise, the lattice dynamics...

have also found application as Wannier functions in the study of solids. The IBO method entails molecular wave-functions calculated using self-consistent...

orbitals in systems with periodic boundary conditions are known as Wannier functions. Standard ab initio quantum chemistry methods lead to delocalized...

calculations Efficient implementation of Van der Waals functional Wannier function implementation TranSIESTA/TBTrans module with any number of electrodes...

mass. In the case of Wannier-Mott excitons, the relative motion of electron and hole in the crystal covers many unit cells. Wannier-Mott excitons are considered...

delocalized, symmetry adapted molecular orbitals used in molecules (while Wannier functions correspond to localized molecular orbitals). A number of important...

converge to thin energy bands corresponding to the Landau levels. Gregory Wannier showed that by taking into account the density of states, one can obtain...

cells, and the ϕ R {\displaystyle \phi _{\mathbf {R} }} are known as Wannier functions. The corresponding eigenvalues E ( k ) {\displaystyle E\left(\mathbf...

In mathematics, an involution, involutory function, or self-inverse function is a function f that is its own inverse, f(f(x)) = x for all x in the domain...

real-space wave functions and Lanczos iterative methods PySCF QuantumATK - LCAO and PW methods. Quantum ESPRESSO - Wannier-function pseudopotential method...

acting in the space of control parameters. Geometric phase Hannay angle Wannier function Berry phase Wilson loop Winding number Byers–Yang theorem Aharonov–Casher...

Wannier function, orbital – Gregory Wannier Wasserman 9-Panel Plot – Karlman Wasserman Wannier–Stark ladder (a.k.a. Stark ladder) – Gregory Wannier and...

also possible to extract the Kohn-Sham eigenfunctions in terms of Wannier functions. List of quantum chemistry and solid state physics software Wortmann...

states Electron and spin density Bader charges and critical points Wannier functions Total energies and energy differences Fermi surfaces Optical properties...

spin–orbit effect; see below.) In a crystalline solid, V is a periodic function, with the same periodicity as the crystal lattice. Bloch's theorem proves...

transition and the theory of the Mott insulator. Wannier functions are introduced by Gregory Wannier. Conyers Herring theorizes the possibility of Weyl...

Nernst Walther Ritz Wander Johannes de Haas Wang Ganchang Wang Zhuxi Wannier function Ward Plummer Wardenclyffe Tower Ward–Takahashi identity Warm dark matter...

of non-orthogonal generalized Wannier functions (NGWFs) expressed in terms of periodic cardinal sine (psinc) functions, which are in turn equivalent to...

development of a method for calculating electron-phonon interactions using Wannier functions. These approaches and others first developed for this research are...

sectors, separated domains not linked by finite fluctuations. Kramers and Wannier were able to show that the high-temperature expansion and the low-temperature...

curvature, the correlation function F ~ ( R ) {\displaystyle {\tilde {F}}({\bf {R}})} is a measure of the overlap of Wannier functions centered at two home...

by 66) Kane, E. O. and A. B. Kane (1978). "DIRECT CALCULATION OF WANNIER FUNCTIONS - SI VALENCE BANDS." Physical Review B 17(6): 2691-2704. (cited by...