MATHEMATICS

Variational estimations of the eigenvalues for 3D quantum waveguides in a transverse electric field

D. G. Matveev^a, I. Yu. Popov<sup>b

a</sup> Microsoft, Redmond, WA, USA
^b Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Russia

Abstract: It is shown that an eigenvalue of the Laplacian exists below the continuous spectrum for a system of threedimensional 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 waveguides, external field.

UDC: 517.938

PACS: 05.45.Df, 61.43.Hv, 83.10.Rs

Language: English

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