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Long-range many-body scattering

Asymptotic clustering for coulomb-type potentials

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References

  • [Comb] Combes, J.M.: Relatively compact interactions in many particle systems. Commun. Math. Phys.12, 283 (1969)

    Google Scholar 

  • [CFKS] Cycon, H., Froese, R., Kirsch, W., Simon, B.: Schrödinger operators. Berlin Heidelberg New York: Springer 1987

    Google Scholar 

  • [Der] Derezinski, J.: A new proof of propagation theorem forN-body quantum systems. Viginia Tech. 1988 (Preprint)

  • [En] Enss, V.: Quantum scattering theory for two and three-body systems with potentials of short- and long-range. In: Graffi, S. (ed.) Schrödinger operators. (Lect. Notes Math., Vol. 1159) Berlin Heidelberg New York: Springer 1985

    Google Scholar 

  • [FH] Froese, R., Herbst, I.: A new proof of Mourre estimate. Duke Math. J.49, 1975 (1982)

    Google Scholar 

  • [Ka1] Kato, T.: Fundamental properties of Hamiltonian operators of Schrödinger type. Trans. Am. Math. Soc.70, 195–211 (1951)

    Google Scholar 

  • [Ka2] Kato, T.: Wave operators and similarity for some non-self-adjoint operators. Math. Ann.162, 258–269 (1966)

    Google Scholar 

  • [Mo1] Mourre, E.: Absence of singular continuous spectrum for certain self-adjoint operators. Commun. Math. Phys.78, 391–408 (1981)

    Google Scholar 

  • [Mo2] Mourre, E.: private communication

  • [Pe] Perry, P.: Commun. Math. Phys.81, 243–259 (1981)

    Google Scholar 

  • [PSS] Perry, P., Sigal, I.M., Simon, B.: Spectral analysis ofN-body Schrödinger operators. Ann. Math.114, 519–567 (1981)

    Google Scholar 

  • [RS] Reed, M., Simon, B.: Methods of modern mathematical physics II, III, IV. New York: Academic Press

  • [Sig1] Sigal, I.M.: On the long-range scattering. Toronto (Preprint)

  • [Sig2] Sigal, I.M.: Lectures on scattering theory. Toronto: xxx 1987

  • [SigSof1] Sigal, I.M., Soffer, A.: TheN-particle scattering problem: asymptotic completeness for short-range systems. Anal. Math.125, (1987)

  • [SigSof2] Sigal, I.M., Soffer, A.: Asymptotic completeness of multiparticle scattering. In: Knowles, Saito (eds.) Differential equations and mathematical physics. (Lect. Notes Math., Vol. 1285) Berlin Heidelberg New York: Springer 1987

    Google Scholar 

  • [SigSof3] Sigal, I.M. Soffer, A.: Local decay and velocity bounds. Princeton (1988) (Preprint)

  • [SigSof4] Sigal, I.M., Soffer, A.: Asymptotic completeness for Coulomb-type 4-body systems. (In preparation)

  • [SinMuth] Sinha, K., Muthuramalingam, P.L.: J. Funct. Anal.55, 323–343 (1984)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, M5S1A1, Toronto, Canada

    I. M. Sigal

  2. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    A. Soffer

Authors
  1. I. M. Sigal
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  2. A. Soffer
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Additional information

Supported by NSERC under Grant NA 7901; I. W. Killam Research Fellow

Supported by NSF under Grant DMS85-07040; Alfred Sloan Fellow in Mathematics

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Sigal, I.M., Soffer, A. Long-range many-body scattering. Invent Math 99, 115–143 (1990). https://doi.org/10.1007/BF01234413

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