Costin, O.; Soffer, A. Resonance theory for Schrödinger operators. (English) Zbl 0992.81025 Commun. Math. Phys. 224, No. 1, 133-152 (2001). A modified general theory for resonances resulting form perturbation of embedded eigenvalues is developed. In particular, the Fermi Golden rule is weakened. This allows to study perturbed threshold eigenvalues. The time decay of the resonant states is given as an asymptotic expansion of solutions of the corresponding Schrödinger equation. Reviewer: Michael Demuth (Clausthal) Cited in 23 Documents MSC: 81Q15 Perturbation theories for operators and differential equations in quantum theory 35B34 Resonance in context of PDEs 81U99 Quantum scattering theory 34E05 Asymptotic expansions of solutions to ordinary differential equations 47A55 Perturbation theory of linear operators 47A10 Spectrum, resolvent Keywords:perturbation of embedded eigenvalues; Fermi Golden rule; threshold eigenvalues; time decay of the resonant states; asymptotic expansion PDFBibTeX XMLCite \textit{O. Costin} and \textit{A. Soffer}, Commun. Math. Phys. 224, No. 1, 133--152 (2001; Zbl 0992.81025) Full Text: DOI arXiv