Il Nuovo Cimento (1955-1965)

, Volume 13, Issue 1, pp 231–236 | Cite as

Wave operators in multichannel scattering

  • M. N. Hack
Lettere Alla Redazione


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  1. (1).
    J. M. Jauch:Helv. Phys. Acta,31, 661 (1958).MathSciNetMATHGoogle Scholar
  2. (2).
    J. M. Cook:Journ. Math. Phys.,36, 82 (1957);M. N. Hack:Nuovo Cimento,9, 731 (1958);J. M. Jauch andI. I. Zinnes:Nuovo Cimento,11, 553 (1959);S. T. Kuroda: to be published.Google Scholar
  3. (3).
    S. T. Kuroda: reference (2).Google Scholar
  4. (4).
    M. H. Stone:Linear Transformations in Hilbert Space (New York, 1932), p. 152, Theorem 4.26.Google Scholar
  5. (5).
    T. Kato:Trans. Amer. Math. Soc.,70, 195 (1951).MathSciNetMATHGoogle Scholar
  6. (6).
    See,e.g.,F. Riesz andB. Sz.-Nagy:Functional Analysis (New York, 1955), pp. 384–385.Google Scholar
  7. (7).
    J. M. Jauch: reference (1). The equality ofR + andR (unitarity property of theS-operator) means in the single-channel case that if the condition (2) holds for eithert →−∞ ort →+∞, it holds for both. However the equality ofR +(α) andR (α) will not in general hold in the multichannel case, since by the orthogonality theorem it would exclude scattering into or out of the channel. An exception (cf. Sect.4) is in the channels where all particles are bound.MathSciNetMATHGoogle Scholar
  8. (8).
    This corresponds to the case treated byJ. M. Cook: reference (2), in single-channel scattering.Google Scholar

Copyright information

© Società Italiana di Fisica 1959

Authors and Affiliations

  • M. N. Hack
    • 1
  1. 1.Argonne National LaboratoryLemont

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