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Communications in Mathematical Physics

, Volume 67, Issue 1, pp 85–90 | Cite as

On the Cook-Kuroda criterion in scattering theory

  • Tosio Kato
Article

Abstract

A new criterion of the Cook-Kuroda type for the existence of the wave operator in the two-space scattering theory is introduced. The condition is quite simple, but it generalizes not only the original Cook-Kuroda condition but also its generalization recently given by Schechter. Specialized to the one-space case, it is actually equivalent to Schechter's condition for an optimal choice of factorization. An application to potential scattering leads to a new result.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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References

  1. 1.
    Schechter, M.: A new criterion for scattering theory. Duke Math. J.44, 863–872 (1977)Google Scholar
  2. 2.
    Simon, B.: Scattering theory and quadratic forms: On a theorem of Schechter. Commun. Math. Phys.53, 151–153 (1977)Google Scholar
  3. 3.
    Cook, J.M.: Convergence to the Møller wave-matrix. J. Math. Phys.36, 82–87 (1957)Google Scholar
  4. 4.
    Kuroda, S.T.: On the existence and the unitary property of the scattering operator. Nuovo Cimento12, 431–454 (1959)Google Scholar
  5. 5.
    Kato, T.: Scattering theory with two Hilbert spaces. J. Funct. Anal.1, 342–369 (1967)Google Scholar
  6. 6.
    Kato, T.: A second look at the essential selfadjointness of the Schrödinger operators. In: Physical reality and mathematical description, pp. 193–201. Dortrecht: Reidel 1974Google Scholar
  7. 7.
    Kato, T.: Perturbation theory for linear operators, 2nd ed. Heidelberg, New York: Springer 1976Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Tosio Kato
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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