Communications in Mathematical Physics

, Volume 63, Issue 3, pp 277–301 | Cite as

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

  • E. B. Davies
  • B. Simon
Article
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Abstract

We discuss the existence and completeness of scattering for one-dimensional systems with different spatial asymptotics at ±∞, for example −d2/dx2+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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • E. B. Davies
    • 1
  • B. Simon
    • 1
    • 2
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of PhysicsPrinceton UniversityUSA

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