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Studying unitary one-parameter groups in Hilbert space (U(t), H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U(t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator and scattering matrix. We illustrate our results in the Lax-Phillips model where (U(t), H) represents an acoustic wave equation in an exterior domain; and in quantum tunneling for dynamics of quantum states.


Copyright © 2012, American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics 53.5, and may be found at