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    • Schrödinger operators on the half line: Resolvent expansions and the Fermi golden rule at thresholds

      Arne Jensen Gheorghe Nenciu

      Scattering Theory Volume 116 Issue 4 November 2006 pp 375-392

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      https://www.ias.ac.in/article/fulltext/pmsc/116/04/0375-0392

    • Keywords

       

      Schrödinger operator; threshold eigenvalue; resonance; Fermi golden rule

    • Abstract

       

      We consider Schrodinger operatorsH = - d2 /dr2 +V onL2([0, ∞)) with the Dirichlet boundary condition. The potentialV may be local or non-local, with polynomial decay at infinity. The point zero in the spectrum ofH is classified, and asymptotic expansions of the resolvent around zero are obtained, with explicit expressions for the leading coefficients. These results are applied to the perturbation of an eigenvalue embedded at zero, and the corresponding modified form of the Fermi golden rule.

    • Author Affiliations

       

      Arne Jensen1 Gheorghe Nenciu2 3

      1. Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, Aalborg Ø - DK-9220, Denmark
      2. Department of Theoretical Physics, University of Bucharest, P. O. Box MG11, Bucharest - 76900, Romania
      3. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P. O. Box 1-764, Bucharest - RO-014700, Romania

    • Dates

       
      Published
      November 2006

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