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Scattering theory for systems with different spatial asymptotics on the left and right

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Abstract

We discuss the existence and completeness of scattering for one-dimensional systems with different spatial asymptotics at ±∞, for example −d 2/dx 2+V(x) whereV(x)=0 (resp. sinx) ifx<0 (resp.x>0). We then extend our results to higher dimensional systems periodic, except for a localised impurity, in all but one space dimension. A new method, “the twisting trick”, is presented for proving the absence of singular continuous spectrum, and some independent applications of this trick are given in an appendix.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, New Jersey, USA

    E. B. Davies & B. Simon

  2. Department of Physics, Princeton University, USA

    B. Simon

Authors
  1. E. B. Davies
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  2. B. Simon
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Additional information

Communicated by J. Ginibre

Research supported by NSF grant MPS-75-11864

On leave from Mathematical Institute, Oxford OX1 3JP, England

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Davies, E.B., Simon, B. Scattering theory for systems with different spatial asymptotics on the left and right. Commun.Math. Phys. 63, 277–301 (1978). https://doi.org/10.1007/BF01196937

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  • DOI: https://doi.org/10.1007/BF01196937

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