| The spectral analysis of the Schr"odinger operator on cubic lattice type graphs is developed. Similarly to the quantum mechanical tight-binding approximation, using the well known conception of the Dirichlet-to-Neumann map asymptotic formulae for localized negative spectral bands of the Schr"odinger operator on a periodic metric graph are established. The results are illustrated by numerical calculations. |
Keywords
the Schr"odinger operator, a metric graph, the Dirichlet-to-Neumann map, a spectral band
Math Review Classification
Primary 81Q10
; Secondary 34L40
Last Updated
3/12/03
Length
37 pages
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