We give a sufficient condition for the existence of an eigenvalue below the lower bound π2 of the continuous spectrum in a two-dimensional quantum waveguide composed from two semi-strips of width 1 and 1 - ε with the junction zone of width 1+O(ε). This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when ε → 0+.
Asymptotic analysis of an eigenvalue in the discrete spectrum of a quantum waveguide / Cardone, G. - 1558:(2013), pp. 1809-1812. (Intervento presentato al convegno 11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013 tenutosi a Rhodes; Greece nel 21/09/2013 - 27/09/2013) [10.1063/1.4825877].
Asymptotic analysis of an eigenvalue in the discrete spectrum of a quantum waveguide
Cardone G
2013
Abstract
We give a sufficient condition for the existence of an eigenvalue below the lower bound π2 of the continuous spectrum in a two-dimensional quantum waveguide composed from two semi-strips of width 1 and 1 - ε with the junction zone of width 1+O(ε). This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when ε → 0+.| File | Dimensione | Formato | |
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