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Analyticity in the coupling constant and bound states in potential theory

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Il Nuovo Cimento (1955-1965)

Summary

A method for determining the wave function in potential scattering from theS-matrix, using unitarity and analyticity, is extended to the case where bound states are present by using analytic continuation in the coupling constant. A numerical example is given, illustrating the passage of a pole from the second Riemann sheet of the energy to the first sheet.

Riassunto

Un metodo precedentemente proposto per la determinazione della funzione d’onda nella teoria dello scattering da potenziale usando l’analiticità e l’unitarietà è esteso al caso in cui sono presenti stati legati, facendo uso della continuazione analitica nella costante d’accoppiamento. È dato un esempio esplicito ad illustrazione dello spostamento di un polo dal secondo foglietto di Riemann dell’energia al primo.

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References

  1. I. M. Gel’fand andB. M. Levitan:Dokl. Akad. Nauk S.S.S.R.,77, 557 (1951);Izvest. Akad. Nauk S.S.S.R.,45, 309 (1951) and Ref. (6).

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  2. B. Bosco:Nuovo Cimento,17, 558 (1960), hereafter referred to as (B).

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  3. For a statement of Poincaré’s theorems, seee.g.,R. G. Newton:Journ. Math. Phys.,1, 319 (1960).

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  4. R. Jost andA. Pais:Phys. Rev.,82, 840 (1951). A potential can give rise to bound-states only if\(\int\limits_0^\infty {r|V(r)|} {\text{d}}r \geqslant 1\).

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  5. See for exampleR. Jost andW. Kohn:Dan. Mat. Fys. Medd.,27, 9 (1953), Footnote (6).

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  6. See Ref. (6).

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  7. R. Jost:Helv. Phys. Acta,20, 256 (1947);H. A. Bethe andR. Bacher:Rev. Mod. Phys.,8, 111 (1936);S. T. Ma:Phys. Rev.,69, 668 (1946).

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Author notes

  1. B. Bosco

    Present address: Istituto di Fisica dell’Università, Torino, Italy

  2. J. Sucher

    Present address: University of Maryland, College Park, Md.

Authors and Affiliations

  1. Brookhaven National Laboratory, Upton, N. Y.

    B. Bosco

  2. Institute of Theoretical Physics, Stanford University, Stanford, California

    J. Sucher

Authors
  1. B. Bosco
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  2. J. Sucher
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Additional information

Supported in part by the United States Atomic Energy Commission and by the United States Air Force.

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Bosco, B., Sucher, J. Analyticity in the coupling constant and bound states in potential theory. Nuovo Cim 19, 1183–1188 (1961). https://doi.org/10.1007/BF02731393

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  • DOI: https://doi.org/10.1007/BF02731393

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