Open Access2D waveguides: asymptotics of eigenvalue induced by a window in a semitransparent separating wall
Author(s) -
Игорь Юрьевич Попов,
AUTHOR_ID,
Ekaterina Trifanova,
AUTHOR_ID
Publication year - 2021
Publication title -
bulletin of the "transilvania" university of braşov. series iii, mathematics and computer science
Language(s) - English
Resource type - Journals
eISSN - 2810-2037
pISSN - 2810-2029
DOI - 10.31926/but.mif.2021.1.63.1.15
Subject(s) - eigenvalues and eigenvectors , hypersurface , window (computing) , waveguide , term (time) , physics , optics , mathematical analysis , mathematics , quantum mechanics , computer science , operating system
Two-dimensional quantum waveguides with common semitransparent wallare considered. It is assumed that there is a small window in the separat-ing wall. It leads to the appearance of an eigenvalue below the continuousspectrum. Semitransparent wall is introduced as a potential supported bya hypersurface. We use the method of asymptotic expansions of boundaryproblems solutions. It allows us to obtain the main term of the asymptoticsexplicitly