Rashba, EmmanuelZhukov, L. E.Efros, A. L.2016-11-181997Rashba, E. I., L. E. Zhukov, and A. L. Efros. 1997. Orthogonal Localized Wave Functions of an Electron in a Magnetic Field. Physical Review B. doi:10.1103/physrevb.55.5306.0163-1829http://nrs.harvard.edu/urn-3:HUL.InstRepos:29407072We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized at the origin has a nearly Gaussian shape of exp(-r^2/4l^2)/sqrt(2Pi) for r < sqrt(2Pi)l,where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w_{00}(r) is small, oscillates, and falls off with the Thouless critical exponent for magnetic orbitals, r^(-2). These functions form a convenient basis for many electron problems.en-USJournal Article2016-11-1810.1103/PhysRevB.55.5306