un 1 99 6 Orthogonal localized wave functions of an electron in a magnetic field
نویسنده
چکیده
We prove the existence of a set of two-scale magnetic Wannier orbitals, wmn(r), in the infinite plane. The quantum numbers of these states are the positions (m,n) of their centers which form a von Neumann lattice. Function w00(r) localized at the origin has a nearly Gaussian shape of exp(−r2/4l2)/ √ 2π for r ∼ √ 2πl, where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w00(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. 71.70.Di, 73.20.Dx Typeset using REVTEX 1
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ar X iv : c on d - m at / 9 60 30 37 v 1 6 M ar 1 99 6 Orthogonal localized wave functions of an electron in a magnetic field
A complete set of localized orthogonal wave functions for an electron at the lowest Landau level is found. The quantum numbers of these states are the positions of their centers which form a von Neumann lattice. The function localized at the origin has a nearly Gaussian shape exp(−r2/4l2)/ √ 2π for r ∼ √ 2πl. However, it oscillates and decreases as r for r ∼ √ 2πl; l is the magnetic length. The...
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