Volume 47, Number 1, January-February 2013
|Page(s)||305 - 315|
|Published online||23 November 2012|
Bound states of a converging quantum waveguide
University of Sannio - Department of Engineering,
Piazza Roma, 21, 84100
2 Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178 St. Petersburg, Russia
3 University of Oulu - Department of Electrical Engineering, P.O. Box 4500, 90014 Oulu, Finland
Revised: 14 May 2012
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+.
Mathematics Subject Classification: 35P15 / 47A75 / 49R50
Key words: Quantum waveguide / spectrum / asymptotics
© EDP Sciences, SMAI, 2012
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