Wigner–von Neumann perturbations of a periodic potential: spectral singularities in bands
Wigner–von Neumann perturbations of a periodic potential: spectral singularities in bands
复制标题
周期性势的维格纳-冯·诺依曼扰动：带中的光谱奇点
DOI：
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发表时间：
2007
影响因子：
0.8
通讯作者：
S. Naboko
中科院分区：
文献类型：
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作者：
P. Kurasov;S. Naboko
摘要 考虑周期性一维薛定谔算子的维格纳-冯诺依曼型扰动。研究了广义特征函数方程解的渐近性。事实证明，在满足扰动频率、背景电势频率和相应准动量之间一定共振（量化）条件的绝对连续谱的点处，可能会出现从属解，从而产生嵌入特征值。
Abstract Wigner–von Neumann type perturbations of the periodic one-dimensional Schrödinger operator are considered. The asymptotics of the solution to the generalized eigenfunction equation is investigated. It is proven that a subordinated solution and therefore an embedded eigenvalue may occur at the points of the absolutely continuous spectrum satisfying a certain resonance (quantization) condition between the frequencies of the perturbation, the frequency of the background potential and the corresponding quasimomentum.