Analysis of superlattice structure using spectal analysis of Schroedinger operator

研究了超晶格半导体器件的一些数学模型的光谱结构。我们的结果如下：研究了点相互作用薛定谔算子的特征值个数。在一维情形下，我们将一些约束条件下的已知结果推广到没有约束条件的情形。在二维和三维情况下，虽然任何结果都是未知的，但我们得到了新的结果。我们可以处理这些模型的离散版本。我们在一维情形下得到了类似的结果，并证明了在多维情形下对双曲性的依赖性。

We studied spectral structure of some mathematical model of superlattice semiconductor device. Our results are as follows ; we studied the number of eigenvalues of Schroedinger operator with point interactions. In one dimensional case, we extended the known results under some restrictions to the ones without the restrictions. In two and three dimensional cases, though any results are unknown, we obtained the new results. We can treat discrete version of these models. We obtained similar results in one dimensional case and proved the dependence on the hyperbolicity in multidimensional cases.