泄漏量子线和量子点的共振模型
Leaky quantum wire and dots: a resonance model
摘要：
讨论了$L^2(\mathbb{R}^2)$中由Laplacian描述的具有吸引奇异微扰的漏量子线和一族量子点的模型。的离散谱被证明是非空的，而且，共振问题可以明确地解决在这种设置，通过Birman-Schwinger方法，它被重新制定成一个弗里德里希型模型。
英文摘要：
We discuss a model of a leaky quantum wire and a family of quantum dots described by Laplacian in $L^2(\mathbb{R}^2)$ with an attractive singular perturbation supported by a line and a finite number of points. The discrete spectrum is shown to be nonempty, and furthermore, the resonance problem can be explicitly solved in this setting; by Birman-Schwinger method it is reformulated into a Friedrichs-type model.
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