NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2012, 3 (3), P. 6–22
VARIATIONAL ESTIMATIONS OF THE EIGENVALUES FOR 3D QUANTUM WAVEGUIDES IN A TRANSVERSE ELECTRIC FIELD
D.G. Matveev – Microsoft, Redmond, WA, USA, d.g.matveev@gmail.com
I.Yu. Popov – Saint-Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint-Petersburg, Russia, professor, D.Sc., popov1955@gmail.com
It is shown that an eigenvalue of the Laplacian exists below the continuous spectrum for a system of three-dimensional quantum waveguides laterally coupled via a small window and placed in a transverse electric field, and the estimation for the eigenvalue is obtained. A field induced shift of the eigenvalue is estimated by using a variation.
Keywords: variational method, spectrum estimations, quantum wavequides, external field.
UDC 517.938
PACS 05.45.Df, 61.43.Hv, 83.10.Rs
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