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...

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

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

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

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

basis code NanoGW - real-space wave functions and Lanczos iterative methods PySCF Quantum ESPRESSO - Wannier-function pseudopotential method Questaal -...

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

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

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

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

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

postprocessing situations it may be useful to project Kohn-Sham states onto Wannier functions. For the LAPW method such projections have also been implemented and...

excitons are called Wannier-Mott excitons, for which the relative motion of electron and hole in the crystal covers many unit cells. Wannier-Mott excitons are...

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

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...

thermodynamic integration Efficient computation of maximally localized Wannier functions GGA and hybrid density functional approximations (LDA, PBE, SCAN,...

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

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

used to write the partition function into a simpler form. It was introduced in 1941 by Hans Kramers and Gregory Wannier. In many one dimensional lattice...

^{3}F(\nu /T)} for some function F of a single variable. A modern variant of Wien's derivation can be found in the textbook by Wannier and in a paper by E...

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...

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...

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

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

interactions. They postulate the Mott insulator. Wannier functions are introduced by Gregory Wannier. Conyers Herring theorizes the possibility of Weyl...

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...