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We prove the existence of a set of two-scale magnetic Wannier orbitalsw_{m,n}(r) on the infinite plane. The quantum numbers of these states are thepositions {m,n} of their centers which form a von Neumann lattice. Functionw_{00}localized at the origin has a nearly Gaussian shape ofexp(-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 offwith the Thouless critical exponent for magnetic orbitals, r^(-2). Thesefunctions form a convenient basis for many electron problems.Comment: RevTex, 18 pages, 5 ps fi

Orthogonal localized wave functions of an electron in a magnetic field