Orthogonal localized wave functions of an electron in a magnetic field

Details Orthogonal localized wave functions of an electron in a magnetic field Orthogonal localized wave functions of an electron in a magnetic field

1996-03-06

arxiv.org/abs/cond-mat/9603037v3

Physics

Condensed Matter

RevTex, 18 pages, 5 ps fig

Scientific paper

10.1103/PhysRevB.55.5306

We 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.

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