Widths of highly excited shape resonances
classification
🧮 math-ph
math.MP
keywords
widthsresonancesshapewellbehaviorbottomboundcase
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We study the widths of shape resonances for the semiclassical multi-dimensional Schr\"odinger operator, in the case where the frequency remains close to some value strictly larger than the bottom of the well. Under a condition on the behavior of the resonant state inside the well, we obtain an optimal lower bound for the widths.
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