Analysis of the Dispersion Equation for the Schr"odinger Operator on Periodic Metric Graphs

V.L. Oleinik, B.S. Pavlov, and N.V. Sibirev


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.

the Schr"odinger operator, a metric graph, the Dirichlet-to-Neumann map, a spectral band

Math Review Classification
Primary 81Q10 ; Secondary 34L40

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37 pages

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