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本文将量子力学中关于厄米算符的一些熟知结论推广至非厄米算符情形。具体地，(1)给出了满足代数方程的非厄米算符的本征值结构；(2)针对一类可对角化的非厄米算符，阐明了对易性、简并子空间，以及块对角化之间的关系，给出了其可视化的图像；(3)以四格点自旋-1/2海森堡XXZ链为例具体说明了这些扩展结果的物理内涵和应用。
Abstract：This paper extends some well-known conclusions about Hermitian operators in quantum mechanics to the case of non-Hermitian operators. Specifically,(1) it presents the eigenvalue structure of non-Hermitian operators satisfying algebraic equations;(2) for a class of diagonalizable non-Hermitian operators, it clarifies the relationship between commutativity, degenerate subspaces, and block diagonalization, and provides a visual representation;(3) taking the four-site spin-1/2 Heisenberg XXZ chain as an example, it specifically illustrates the physical implications and applications of these extended results.
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(1)本例中的F为晶格动量算符,可通过将自旋链费米子化后在费米子模型的动量空间中写出,但这超出了本文的讨论范围。
基本信息:
DOI：
中图分类号:O413.1
引用信息:
[1]娄欣岚,徐大智,吴宁.一些关于厄米算符的结论至非厄米情形的扩展[J].物理与工程,2025,35(05):34-42.
基金信息:
科技部科技创新2030重大项目(2023ZD0300703); 北京理工大学物理学院教改项目“科研成果融入本科量子力学教学”