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Definition and existence of multichannel scattering states

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Abstract

The field theoretical formulation of quantum mechanics is used to consider the nonrelativistic multichannel scattering theory. With the help of appropriately constructed time dependent creation operators, Hilbert vectors are formed whose limits in time can be defined as multichannel scattering states in the usual sense. The existence of these states is proved under certain assumptions for the potential, by showing the convergence of the above mentioned operators. The commutation relations for the limits of these operators are given.

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References

  1. Ekstein, H.: Phys. Rev.101, 880 (1956); Nuovo cimento4, 1017 (1956).

    Google Scholar 

  2. Jauch, J. M.: Helv. Phys. Acta31, 661 (1958).

    Google Scholar 

  3. Hack, M. N.: Nuovo cimento13, 231 (1959).

    Google Scholar 

  4. Brenig, W., andR. Haag: Fortschr. Phys.7, 183 (1959).

    Google Scholar 

  5. Haag, R.: Phys. Rev.112, 669 (1958).

    Google Scholar 

  6. Ruelle, D.: Helv. Phys. Acta35, 147 (1962).

    Google Scholar 

  7. Cook, J. M.: J. Math. and Phys.36, 82 (1957).

    Google Scholar 

  8. Hack, M. N.: Nuovo cimento13, 231 (1959).

    Google Scholar 

  9. Hack, M. N.: Nuovo cimento9, 731 (1958).

    Google Scholar 

  10. Schweber, S. S.: An Introduction to Relativistic Quantum Field Theory. Evanston, Ill.: Row, Peterson and Co. 1961.

    Google Scholar 

  11. Ekstein, H.: Nuovo cimento4, 1017 (1956).

    Google Scholar 

  12. Redmond, P. J., andJ. L. Uretsky: Ann. Phys.9, 106 (1960).

    Google Scholar 

  13. Tani, S.: Phys. Rev.117, 252 (1960);121, 346 (1961).

    Google Scholar 

  14. Schweber, S. S., andE. C. G. Sudarshan: Ann. Phys.19, 351 (1962).

    Google Scholar 

  15. Weidlich, W.: Z. Naturforsch.18a, 1266 (1963).

    Google Scholar 

  16. Stichel, P.: Nuclear Physics52, 189 (1964).

    Google Scholar 

  17. Kato, T.: Trans. Am. Math. Soc.70, 195 (1951).

    Google Scholar 

  18. Schwartz, L.: Théorie des distributions. Vol. II, p. 89ff. Paris: Hermann 1959.

    Google Scholar 

  19. Dollard, J. D.: J. Math. Phys.5, 729 (1964).

    Google Scholar 

  20. Blochinzew, D. I.: Grundlagen der Quantenmechanik, p. 372ff. and p. 532f. Berlin: Deutscher Verlag der Wissenschaften 1953.

    Google Scholar 

  21. Kuroda, S. T.: Nuovo cimento12, 431 (1959).

    Google Scholar 

  22. Kupsch, J., andW. Sandhas: Commun. Math. Phys.2, 147 (1966).

    Google Scholar 

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  1. Werner Sandhas

    Present address: Physikalisches Institut der Universität Bonn, Germany

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  1. Institut für Theoretische Physik der Freien Universität Berlin, Germany

    Werner Sandhas

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  1. Werner Sandhas
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Sandhas, W. Definition and existence of multichannel scattering states. Commun.Math. Phys. 3, 358–374 (1966). https://doi.org/10.1007/BF01645088

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