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
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+.
asymptotic analysis; discrete spectrum; quantum waveguide
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12070/12801
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