标题： 二维中的负特征值的持续与消失 显示英文标题

标题： Persistence and disappearance of negative eigenvalues in dimension two

摘要： 我们计算了二维Schrödinger算子连续谱底部附近特征值及其相关共振的渐进行为。 我们区分了具有相关共振的持久特征值和没有共振的消失特征值。 我们通过计算相应的散射相位渐进行为和数值Breit--Wigner峰来说明这种区别的重要性。 我们证明了所有结果适用于圆形势阱，并利用最近的预解技术将其中一些结果推广到更一般的问题。 显示英文摘要

摘要： We compute asymptotics of eigenvalues approaching the bottom of the continuous spectrum, and associated resonances, for Schr\"odinger operators in dimension two. We distinguish persistent eigenvalues, which have associated resonances, from disappearing ones, which do not. We illustrate the significance of this distinction by computing corresponding scattering phase asymptotics and numerical Breit--Wigner peaks. We prove all of our results for circular wells, and extend some of them to more general problems using recent resolvent techniques.