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Resonances and Virtual Poles in Scattering Theory

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Abstract

Sufficient criteria for the coincidence of resonances and nonreal virtual poles in scattering systems are presented. A Gelfand triplet is constructed such that eigenfunctionals of the extended Hamiltonian exist exactly for the resonances.

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References

  • Baumgärtel, H. (1976). Resonances of Perturbed selfadjoint operators and their Eigenfunctionals. Mathematische Nachrichten 75, 133-151.

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  • Baumgärtel, H. and Wollenberg, M. (1983). Mathematical Scattering Theory, Birkhäuser, Boston, MA.

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  • Gochberg, I. C. and Krein, M. G. (1957). The basic propositions on defect numbers, root numbers and indices of linear operators. Uspekhi Matematicheskikh Nauk 12, 43-118. (In Russian)

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Authors and Affiliations

  1. Mathematical Institute, University of Potsdam Am Neuen Palais 10, Postfach 601 553, D-14415, Potsdam, Germany

    H. Baumgärtel

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  1. H. Baumgärtel
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Baumgärtel, H. Resonances and Virtual Poles in Scattering Theory. International Journal of Theoretical Physics 42, 2379–2388 (2003). https://doi.org/10.1023/B:IJTP.0000005964.63952.46

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  • DOI: https://doi.org/10.1023/B:IJTP.0000005964.63952.46

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