Abstract
A pair of coupled quantum waveguides with a common semitransparent boundary having a small aperture is considered, which leads to resonance phenomena during the passage of an electron. Using the method of matching asymptotic expansions, formulas are obtained for the first terms in the expansions of resonances (quasi-eigenvalues) and resonance states. The influence of the geometry of the system and the transparency parameter of the boundary on the lifetime of resonance states is investigated
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