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The Y‐junction of quantum waveguides
Author(s) -
Nazarov S.A.,
Ruotsalainen K.,
Uusitalo P.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200255
Subject(s) - strips , planar , spectrum (functional analysis) , eigenvalues and eigenvectors , quantum , discrete spectrum , waveguide , physics , continuous spectrum , mathematics , optics , quantum mechanics , computer science , computer graphics (images) , algorithm
A planar quantum waveguide is composed from two semi‐strips of width 1 and a semi‐strip of width H and the angle between strips is 2π/3. The spectrum of the Dirichlet problem in this waveguide is investigated. In particular, it is proved that there exists a critical width H * for which the discrete spectrum is non‐empty for any H ≤ H * and conversely is empty for any H ≥ H * . The critical width is estimated to be approximately H * ≈ 1.25. Furthermore, the eigenvalue in the discrete spectrum is unique for 0 ≤ H≤ H * .
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