For a bounded open domain with connected complement in R 2 and piecewise smooth boundary, we consider the Dirichlet Laplacian on and the S-matrix on the complement c . We show that the on-shell S-matrices S k have eigenvalues converging to 1 as k " k 0 exactly when has an eigenvalue at energy k 2 0 . This includes multiplicities, and proves a weak form of "transparency" at k = k 0 . We also show that stronger forms of transparency, such as S k 0 having an eigenvalue 1 are not expected to hold in general.In th…
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