# Bound states of a converging quantum waveguide

Giuseppe Cardone; Sergei A. Nazarov; Keijo Ruotsalainen

- Volume: 47, Issue: 1, page 305-315
- ISSN: 0764-583X

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topCardone, Giuseppe, Nazarov, Sergei A., and Ruotsalainen, Keijo. "Bound states of a converging quantum waveguide." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.1 (2013): 305-315. <http://eudml.org/doc/273154>.

@article{Cardone2013,

abstract = {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+.},

author = {Cardone, Giuseppe, Nazarov, Sergei A., Ruotsalainen, Keijo},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {quantum waveguide; spectrum; asymptotics},

language = {eng},

number = {1},

pages = {305-315},

publisher = {EDP-Sciences},

title = {Bound states of a converging quantum waveguide},

url = {http://eudml.org/doc/273154},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Cardone, Giuseppe

AU - Nazarov, Sergei A.

AU - Ruotsalainen, Keijo

TI - Bound states of a converging quantum waveguide

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 1

SP - 305

EP - 315

AB - 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+.

LA - eng

KW - quantum waveguide; spectrum; asymptotics

UR - http://eudml.org/doc/273154

ER -

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