Scattering Resonances for a Two-Dimensional Potential Well with a Thick Barrier
Scattering Resonances for a Two-Dimensional Potential Well with a Thick Barrier
复制标题
具有厚势垒的二维势井的散射共振
DOI：
10.1137/140952053
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
F. Santosa
中科院分区：
文献类型：
--
作者：
Junshan Lin;F. Santosa
本文关注$\mathbb{R}^2$中薛定谔算子$-\Delta + V_L$的散射共振。实值势 $V_L$ 是一个低能井，周围环绕着势垒，势垒的有限厚度与 $L$ 成正比。我们感兴趣的是接近与具有无限厚势垒的势相关的非简并束缚态频率的共振。特别是，它表明共振和相关束缚态频率之间的差异作为势垒厚度的函数呈指数衰减，衰减率为 $L^2e^{-cL}$。该分析得出了一种精确逼近近束缚态共振的微扰方法。
This paper is concerned with the scattering resonances of the Schrodinger operator $-\Delta + V_L$ in $\mathbb{R}^2$. The real valued potential $V_L$ is a low energy well surrounded by a barrier with finite thickness proportional to $L$. We are interested in the resonances that are close to the nondegenerate bound state frequencies associated with the potential that has infinitely thick barrier. In particular, it is shown that the difference between a resonance and the associated bound state frequency decays exponentially as a function of the barrier thickness with a rate of $L^2e^{-cL}$. The analysis leads to a perturbative approach for accurately approximating the near bound-state resonances.