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Resonance theory for Schrödinger operators. (English) Zbl 0992.81025

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.

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
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