论文标题
具有光势的施罗宾格运营商的光谱分析
Spectral Analysis of the Schrodinger Operator with an Optical Potential
论文作者
论文摘要
在本文中，我们对Schrodinger Operator L（V）的光谱分析进行了完整描述。首先，我们考虑L（V）的Bolch特征值和频谱。然后使用它，我们研究了频谱奇异性和基本频谱奇异性（ESS）。我们证明运算符L（V）没有ESS，并且仅当V不是关键点而V是关键点时，并且仅当V是一个关键点。使用它，我们将光谱扩展按临界点的术语进行了分类。最后，我们讨论临界点，提出一些猜想，并描述当V变化时L（V）光谱的变化。
In this paper we give a complete description of the spectral analysis of the Schrodinger operator L(V) with the optical potentil. First we consider the Bolch eigenvalues and spectrum of L(V). Then using it we investigate spectral singularities and essential spectral singularities (ESS). We prove that the operator L(V) has no ESS and has ESS respectively if and only if V is not a critical point and V is a critical point. Using it we classify the spectral expansion in term of the critical points. Finally we discuss the critical points, formulate some conjectures and describe the changes of the spectrum of L(V) when V changes.
