
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��dinger equation. \keywords{Resonances; Time-dependent Schr��dinger equation}
time decay of the resonant states, 35B20, asymptotic expansion, Perturbation theory of linear operators, threshold eigenvalues, 35B40, Perturbation theories for operators and differential equations in quantum theory, FOS: Physical sciences, 81Q15, 81Q15; 81Q10;35B34; 35B20; 35B40, Quantum scattering theory, Mathematical Physics (math-ph), 35B34, Mathematics - Analysis of PDEs, perturbation of embedded eigenvalues, 81Q10, FOS: Mathematics, Resonance in context of PDEs, Spectrum, resolvent, Fermi Golden rule, Asymptotic expansions of solutions to ordinary differential equations, Mathematical Physics, Analysis of PDEs (math.AP)
time decay of the resonant states, 35B20, asymptotic expansion, Perturbation theory of linear operators, threshold eigenvalues, 35B40, Perturbation theories for operators and differential equations in quantum theory, FOS: Physical sciences, 81Q15, 81Q15; 81Q10;35B34; 35B20; 35B40, Quantum scattering theory, Mathematical Physics (math-ph), 35B34, Mathematics - Analysis of PDEs, perturbation of embedded eigenvalues, 81Q10, FOS: Mathematics, Resonance in context of PDEs, Spectrum, resolvent, Fermi Golden rule, Asymptotic expansions of solutions to ordinary differential equations, Mathematical Physics, Analysis of PDEs (math.AP)
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 37 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
