We study the large-time behavior of the solutions to the Schrödinger equation associated with a quickly decaying potential in dimension three. We establish the resolvent expansions at threshold zero and near positive resonances. The large-time expansions of solutions are obtained under different conditions, including the existence of positive resonances and zero resonance or/and zero eigenvalue.

中文翻译：

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具有复数值势的Schrödinger方程解的长时间行为

我们研究了Schrödinger方程解与3维快速衰减电位相关的长时间行为。我们在零阈值和接近正共振处建立可分辨的扩展。在不同条件下获得解的长时间扩展，包括存在正共振和零共振或/和零特征值。