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Il Nuovo Cimento (1955-1965)

, Volume 13, Issue 6, pp 1065–1073 | Cite as

Re-arrangement collision matrix

  • G. Mohan
Article

Summary

A study of the rearrangement collision matrix, under certain asymptotic assumptions is made. It is found that although the «asymptotic states» are non-orthogonal, by a proper choice an orthogonal and complete set of physical states with prescribed asymptotic properties can be constructed. Identity of different expressions of the collision matrix is re-derived. Finally, by the help of the collision matrix the state vector itself is expressed in a form where the incoming and outgoing waves into various channels are explicitly separated without putting any configuration space restrictions.

Riassunto

Si studia la matrice di collisione di riordinamento, in determinate condizioni asintotiche. Si trova che, benchè gli «stati asintotici» non siano ortogonali, con una scelta appropriata si può costruire un sistema completo di stati fisici con proprietà asintotiche assegnate. Si rideriva l’identità di differenti espressioni della matrice di collisione. Infine, con l’ausilio della matrice di collisione, il vettore di stato si esprime in una forma in cui le onde entranti e uscenti da vari canali sono separate esplicitamente senza porre alcuna restrizione allo spazio delle configurazioni.

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References

  1. (1).
    For some of the recent developments in this subject seeR. C. Newton:Ann. Phys.,4, 29 (1958);E. Gerjouy:Ann. Phys.,5, 58 (1958). The last mentioned contains a good list of references to earlier work.ADSCrossRefMATHGoogle Scholar
  2. (2).
    CompareA. M. Lane andR. G. Thomas:Rev. Mod. Phys.,30, 257 (1958).MathSciNetADSCrossRefMATHGoogle Scholar
  3. (3).
    B. A. Lippmann andJ. Schwinger:Phys. Rev.,79, 469 (1950).MathSciNetADSCrossRefMATHGoogle Scholar
  4. (4).
    B. A. Lippmann:Phys. Rev.,102, 264 (1956).ADSCrossRefMATHGoogle Scholar
  5. (5).
    L. L. Foldy andW. Tobocman:Phys. Rev.,105, 1099 (1957).ADSCrossRefMATHGoogle Scholar
  6. (6).
    S. T. Epstein:Phys. Rev.,106, 598 (1957).ADSCrossRefMATHGoogle Scholar
  7. (*).
    A vector denoted by the form |〉 or |〉+ will always be regarded η-dependent. See references (5) and (6).Google Scholar

Copyright information

© Società Italiana di Fisica 1959

Authors and Affiliations

  • G. Mohan
    • 1
  1. 1.National Physical LaboratoryNew Delhi

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