标题： 关于一维扰动离散薛定谔方程的谱 显示英文标题

标题： On the spectrum of discrete Schrödinger equation with one-dimensional perturbation

摘要： 我们考虑带有的一维扰动的离散薛定谔方程的谱。 我们得到了散射矩阵的显式形式，并找到了谱的奇异部分不存在的精确条件。 我们还计算了如果此条件不成立时出现的本征值。 在论文的最后一部分，我们对二维扰动的情况给出了一些备注。 显示英文摘要

摘要： We consider the spectrum of the discrete Schr\"odinger equation with one-dimensional perturbation. We obtain the explicit form of scattering matrix and find the exact condition of absence of singular part of the spectrum. We calculated also the eigenvalue that appears if this condition is not true. In the last part of our paper we give few remarks on the case of two-dimensional perturbations.