Abstract
In this paper, we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths ℓ± separated by a window of length 2a. It is known that if the barriers are semi-infinite, i.e., we have two adjacent waveguides coupled laterally through the boundary window, the system has for any a > 0 a finite number of eigenvalues below the essential spectrum threshold. Here, we demonstrate that for large but finite ℓ± the system has resonances which converge to the said eigenvalues as ℓ± → ∞, and derive the leading term in the corresponding asymptotic expansion.
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