Bound states of a converging quantum waveguide
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 (2013) no. 1, pp. 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: 10.1051/m2an/2012033
Classification: 35P15, 47A75, 49R50
Keywords: quantum waveguide, spectrum, asymptotics
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Cardone, Giuseppe; Nazarov, Sergei A.; Ruotsalainen, Keijo. Bound states of a converging quantum waveguide. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 (2013) no. 1, pp. 305-315. doi : 10.1051/m2an/2012033. http://www.numdam.org/articles/10.1051/m2an/2012033/

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