Il Nuovo Cimento (1955-1965)

, Volume 28, Issue 5, pp 1066–1090 | Cite as

On the existence of the scattering operator

  • N. Limić


The existence of the wave operators and the scattering operator for the scattering on highly singular spherically symmetric potentials that are repulsive at the origin is shown. The eigenfunction expansion in terms of the eigenfunctions of the Hamiltonian is derived using the analytic properties of the solution of the Schrödinger equation.


Si mostra l’esistenza degli operatori d’onda e degli operatori di scattering per lo scattering di potenziali molto singolari a simmetria sferica che sono repulsivi all’origine-Si deduce lo sviluppo dell’autofunzione in funzione delle autofunzioni dell’hamiltoniano, facendo uso delle proprietà analitiche della soluzione dell’equazione di Schrödinger.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    J. M. Cook:Journ. Math. Phys.,36, 82 (1957).Google Scholar
  2. (2).
    M. N. Hack:Nuovo Cimento,9, 731 (1958).CrossRefMATHGoogle Scholar
  3. (3).
    J. M. Jauch andI. I. Zinnes:Nuovo Cimento,11, 553 (1959).MathSciNetCrossRefGoogle Scholar
  4. (4).
    S. T. Kuroda:Nuovo Cimento,12, 431 (1959).CrossRefMATHGoogle Scholar
  5. (5).
    T. A. Green andO. E. Lanford:Journ. Math. Phys.,1, 139 (1960).MathSciNetADSCrossRefMATHGoogle Scholar
  6. (6).
    K. Kodaira:Am. Journ. Math.,71, 921 (1949).MathSciNetCrossRefMATHGoogle Scholar
  7. (7).
    E. C. Titchmarsh:Eigenfunction Expansions (Oxford, 1946).Google Scholar
  8. (8).
    T. Kato:Trans. Am. Math. Soc.,70, 155 (1951).Google Scholar
  9. (9).
    N. Dunpord andJ. T. Schwartz:Linear Operators I (New York, 1958).Google Scholar
  10. (10).
    R. G. Newton:Journ. Math. Phys.,1, 319 (1960).ADSCrossRefMATHGoogle Scholar
  11. (11).
    F. Riesz andB. Sz. Nagt:Vorlesungen über Funktionalanalysis (Berlin, 1956) p. 276.Google Scholar
  12. (12).
    M. A. Naimark:Linear Differential Operators (Russian) (Moscow, 1954).Google Scholar
  13. (13).
    N. Limić:Wuovo Cimento,26, 581 (1962).MATHGoogle Scholar
  14. (14).
    T. Regge:Nuovo Cimento,14, 951 (1959).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Società Italiana di Fisica 1963

Authors and Affiliations

  • N. Limić
    • 1
  1. 1.Institute « Rudjer Bošković »Zagreb

Personalised recommendations