2000/12/31 by Ovidiu Costin, O. Costin, Avy Soffer +1 · 1 citation
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:35B20 #msc:35B34 #msc:35B40 #msc:81Q10 #msc:81Q15
paper · pdf · doi:10.1007/s002200100558
published as Commun. Math. Phys., 224, 133-152 (2001)
openalex publication_date 2001/11/01 · arxiv created 2002/02/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Schrödinger equation. \keywordsResonances; Time-dependent Schrödinger equation