V2EX self-adjoint

Self-adjoint

Definition|释义

(数学/物理)自伴的;自伴算子(或自伴矩阵)的:指一个线性算子(或矩阵)等于它的伴随(共轭转置);在希尔伯特空间中,这种算子对应“可观测量”,其特征值为实数并具有良好的谱性质。(在有限维情形中常与 Hermitian(厄米)密切相关。)

Pronunciation|发音(IPA)

/slf dnt/

Examples|例句

A self-adjoint matrix has real eigenvalues.
自伴矩阵具有实特征值。

To ensure the quantum Hamiltonian represents a physical observable, it must be self-adjoint on an appropriate domain.
为了保证量子哈密顿量能代表物理可观测量,它必须在合适的定义域上是自伴的。

Etymology|词源

self- 表示“自身”,adjoint 源自拉丁语 adiungere(连接、附加),在数学里指“伴随(算子)”。合起来 self-adjoint 字面意思是“自身等于其伴随”,即“与自己的伴随相同”。

Related Words|相关词汇

Literary Works|文学与名著中的用例

  • Methods of Modern Mathematical Physics, Vol. I: Functional Analysis(Reed & Simon):大量讨论自伴算子及其谱理论基础。
  • Functional Analysis(Walter Rudin):在希尔伯特空间框架下系统使用并推导自伴算子相关结论。
  • Quantum Mechanics(Claude Cohen-Tannoudji 等):以“物理可观测量对应自伴算子”为核心表述之一,频繁出现该术语。
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