Geodesic
A discrete Schrödinger operator on a graph
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 1, pp. 119-133 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the discrete Schrödinger operator on the graph obtained in the strong-coupling approximation from the standard electron Schrödinger operator in the system composed of a quantum wire and quantum dot. We investigate the general spectral properties of this operator and the problem of the existence and behavior of the eigenvalues and resonances depending on the small coupling constant. We study the scattering problem for weak potentials in the stationary approach.
Keywords: discrete Schrödinger operator, spectrum, eigenvalue, resonance, scattering problem, quantum wire. 
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Yu. P. Chuburin. A discrete Schrödinger operator on a graph. Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 1, pp. 119-133. http://geodesic.mathdoc.fr/item/TMF_2010_165_1_a6/

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