Bound states of a converging quantum waveguide
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 1, p. 305-315

We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 - ε, where ε > 0 is a small real parameter, i.e. the waveguide is gently converging. The width of the junction zone for the semi-strips is 1 + O(√ε). We will present a sufficient condition for the existence of a weakly coupled bound state below π2, the lower bound of the continuous spectrum. This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when ε → 0+.

DOI : https://doi.org/10.1051/m2an/2012033
Classification:  35P15,  47A75,  49R50
Keywords: quantum waveguide, spectrum, asymptotics
@article{M2AN_2013__47_1_305_0,
author = {Cardone, Giuseppe and Nazarov, Sergei A. and Ruotsalainen, Keijo},
title = {Bound states of a converging quantum waveguide},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {47},
number = {1},
year = {2013},
pages = {305-315},
doi = {10.1051/m2an/2012033},
mrnumber = {2997503},
language = {en},
url = {http://www.numdam.org/item/M2AN_2013__47_1_305_0}
}

Cardone, Giuseppe; Nazarov, Sergei A.; Ruotsalainen, Keijo. Bound states of a converging quantum waveguide. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 1, pp. 305-315. doi : 10.1051/m2an/2012033. http://www.numdam.org/item/M2AN_2013__47_1_305_0/

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