Theory of Simple Scattering and Eigenfunction Expansions

  • Tosio Kato
  • S. T. Kuroda
Chapter

Abstract

In the theory of simple scattering systems we consider the wave operators \({W^ \pm } = \mathop {s - \lim }\limits_{t \to \pm \infty } {e^{it{H_2}}}{e^{ - itH1}}\) and the scattering operator S=(W+)*W­- where H 1 H 2 are selfadjoint operators in a Hilbert space h describing the unperturbed and perturbed systems (see Jauch [12]). W ± are isometric and intertwine H 1 and H 2 (H 2 W ± ⊃ W ± H 1 ) whenever they exist. S is unitary if and only if the ranges of W ± are identical.

Keywords

Unitary Operator Cauchy Sequence Invariance Principle Wave Operator Selfadjoint Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1970

Authors and Affiliations

  • Tosio Kato
    • 1
    • 2
    • 3
  • S. T. Kuroda
    • 1
    • 2
    • 3
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.University of TokyoJapan
  3. 3.Yale UniversityUSA

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