对角无穷维哈密顿算子点谱关于虚轴的对称性

Imaginary Axis Symmetry of the Point Spectrum of the Diagonal Infinite Dimensional Hamiltonian Operators

摘要: 本文将无穷维数Hamilton算子点谱划分为四个部分，得到每个部分的点谱关于虚轴对称的充要条件。运用无穷维数Hamilton算子的谱的结构特点，从而实现了运用内部元素的剩余谱来刻画整体的点谱的关于虚轴的对称性。最后证明了结论的正确性。

Abstract: In this article, the point spectrum of infinite dimension of Hamilton operators is divided into four parts, getting the sufficient and necessary condition about symmetry of each part of the point spectrum. Using structural characteristics of spectrum of infinite dimension of Hamilton operators, then the symmetry axis of the point spectrum is characterized by using the residual spectrum of internal elements. In the end, some examples are constructed to illustrate the effectiveness of criterion.