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On the existence and the unitary property of the scattering operator

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Il Nuovo Cimento (1955-1965)

Summary

The mathematical character of the scattering theory is investigated according to the ≪ time-dependent ≫ formulation with special emphasis on the wave and the scattering operators. The main contents are: 1) some general properties of these operators are summarized; 2) the existence of the wave operator is proved under rather mild conditions on the potential; and 3) the existence and the unitary property of the scattering operator are proved under certain additional conditions. The arguments are mathematically rigorous.

Riassunto

Si esamina il carattere matematico della teoria dello scattering seoondo la formulazione che tien conto della ≪ dipendenza dal tempo ≫ con speciale accento sugli operatori d’onda e di scattering. Gli argomenti principalmente trattati sono i seguenti: 1) si riassumono alcune proprietà generali di detti operatori; 2) si prova l’esistenza dell’operatore d’onda con restrizioni sul potenziale relativamente poco severe; 3) si provano l’esistenza e l’unitarietà dell’operatore di scattering quando siano imposte alcune condizioni addizionali. L’argomentazione è matematicamente rigorosa.

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Authors and Affiliations

  1. Department of Physics, University of Tokyo, Tokyo

    S. T. Kuroda

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  1. S. T. Kuroda
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Traduzione a cura della Redazione.

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Kuroda, S.T. On the existence and the unitary property of the scattering operator. Nuovo Cim 12, 431–454 (1959). https://doi.org/10.1007/BF02745786

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  • DOI: https://doi.org/10.1007/BF02745786

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