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TMF, 2003, Volume 134, Number 3, Pages 341–352 (Mi tmf159)  

This article is cited in 4 scientific papers (total in 4 papers)

Fermi Rule and Scattering Amplitude Resonances

A. A. Arsen'ev

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: The behavior of the scattering amplitude near a resonance with a small imaginary part is investigated. We prove that the scattering amplitude as an energy function suffers a jump near the real part of the resonance and the jump is independent of the interaction details. In terms of the problem data, we derive an estimate for the imaginary part of the resonance.

Keywords: scattering, pole, resonance

DOI: https://doi.org/10.4213/tmf159

Full text: PDF file (236 kB)
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English version:
Theoretical and Mathematical Physics, 2003, 134:3, 296–307

Bibliographic databases:

Received: 07.09.2001
Revised: 12.09.2002

Citation: A. A. Arsen'ev, “Fermi Rule and Scattering Amplitude Resonances”, TMF, 134:3 (2003), 341–352; Theoret. and Math. Phys., 134:3 (2003), 296–307

Citation in format AMSBIB
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\paper Fermi Rule and Scattering Amplitude Resonances
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\pages 341--352
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\zmath{https://zbmath.org/?q=an:1178.81269}
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\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 134
\issue 3
\pages 296--307
\crossref{https://doi.org/10.1023/A:1022689119601}
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  • https://doi.org/10.4213/tmf159
  • http://mi.mathnet.ru/eng/tmf/v134/i3/p341

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Arsen'ev, “Mathematical Model of Resonances and Tunneling in a System with a Bound State”, Theoret. and Math. Phys., 136:3 (2003), 1336–1345  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. A. Arsen'ev, “Relation Between a Pole of the Scattering Matrix and the Transmission and Reflection Coefficients in Scattering in a Quantum Waveguide”, Theoret. and Math. Phys., 140:2 (2004), 1151–1156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. A. Arsen'ev, “Resonances and Tunneling in the Tight-Binding Approximation to Scattering in a Quantum Billiard”, Theoret. and Math. Phys., 141:1 (2004), 1415–1426  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    4. A. A. Arsen'ev, “Resonances and trapped modes in a quantum waveguide”, Comput. Math. Math. Phys., 45:9 (2005), 1573–1581  mathnet  mathscinet  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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