Physics – Condensed Matter – Materials Science
Scientific paper
2007-11-09
Physics
Condensed Matter
Materials Science
8 pages, no figure
Scientific paper
We consider single particle Schrodinger operators with a gap in the energy spectrum. We construct a countable set of exponentially decaying functions, which form a complete, orthonormal basis set for the states below the spectral gap. Each such function is localized near a closed surface. Estimates on the exponential decay rate and a discussion of the geometry of these surfaces is included.
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