Resonance Theory for Schroedinger Operators

Details Resonance Theory for Schroedinger Operators Resonance Theory for Schroedinger Operators

2000-12-08

arxiv.org/abs/math-ph/0012018v3

Commun. Math. Phys., 224, 133-152 (2001)

Physics

Mathematical Physics

Scientific paper

10.1007/s002200100558

Resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods. A general theory is developed, with new and weaker conditions, allowing for perturbations of threshold eigenvalues and relaxed Fermi Golden rule. The exponential decay rate of resonances is addressed; its uniqueness in the time dependent picture is shown is certain cases. The relation to the existence of meromorphic continuation of the properly weighted Green's function to time dependent resonance is further elucidated, by giving an equivalent time dependent asymptotic expansion of the solutions of the Schr\"odinger equation. \keywords{Resonances; Time-dependent Schr\"odinger equation}

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