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Schrödinger operator; threshold eigenvalue; resonance; Fermi golden rule

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.

Arne Jensen¹ Gheorghe Nenciu^{2 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

Published

November 2006