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On The Universal Low Energy Limit in Nonrelativistic Scattering Theory

  • S. Albeverio
  • F. Gesztesy
  • R. Høegh-Krohn
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 23/1981)

Abstract

Based on a precise formulation of the physical intuition that low momenta correspond to large distances we show that scattering quantities have a universal behaviour around the zero energy limit. Our methods rely on unitary implementation of scaling x x/ε, p → εp in the Hilbert space L2 (R3) and on a corresponding expansion of the scattering matrix and amplitude in powers of ε around ε = 0. The results are largely independent of the shape of the interaction, and the leading coefficients in these expansions are described in terms of suitable point interactions.

Keywords

Energy Limit Point Interaction Finite Order Weighted Sobolev Space Scatter Amplitude 
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References

  1. 1.
    S, Albeverio, R. Høegh-Krohn, Point Interactions as Limits of Short Range Interactions, to appear in J. Operator Theory.Google Scholar
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    S. Albeverio, F. Gesztesy, R. Høegh-Krohn, The Low Energy Expansion in Nonrelativistic Scattering Theory, Preprint, Univ. Bielefeld 1981.Google Scholar
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • S. Albeverio
    • 1
  • F. Gesztesy
    • 2
    • 3
  • R. Høegh-Krohn
    • 4
  1. 1.Mathematisches InstitutRuhr-Univ. BochumBochum 1Deutschland
  2. 2.Fakultät für PhysikUniversität BielefeldBielefeld 1Deutschland
  3. 3.Institut für Theoretische PhysikUniversität GrazAustria
  4. 4.Matematisk InstituttUniversitetet i OsloBlindern-Oslo 3Norway

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