V2EX eigenstate

Eigenstate

定义 Definition

eigenstate(本征态/特征态):在量子力学中,指对某个算符(尤其是可观测量算符,如哈密顿量、角动量等)作用时,只会得到一个确定的本征值倍数的量子态。换言之,处于该态时,对应物理量的测量结果是确定的。(也常与“本征值 eigenvalue”成对出现。)

发音 Pronunciation (IPA)

/anstet/

例句 Examples

An eigenstate of the Hamiltonian has a definite energy.
哈密顿量的本征态具有确定的能量。

If the system starts in an eigenstate of the observable, repeated measurements will yield the same eigenvalue (ignoring experimental error).
如果系统一开始处于该可观测量的本征态,那么重复测量将得到相同的本征值(忽略实验误差)。

词源 Etymology

eigen- 来自德语 eigen,意为“自身的、固有的”;在数学与物理中常译作“本征/特征”。state 表示“状态”。因此 eigenstate 字面意思是“固有的状态”,在量子理论中引申为“对应某算符的本征矢/本征态”。

相关词 Related Words

文学与名著用例 Literary Works

  • The Principles of Quantum Mechanics(Dirac,狄拉克《量子力学原理》)
  • Mathematical Foundations of Quantum Mechanics(von Neumann,冯诺依曼《量子力学的数学基础》)
  • Modern Quantum Mechanics(Sakurai & Napolitano,樱井《现代量子力学》)
  • Introduction to Quantum Mechanics(Griffiths & Schroeter,格里菲斯《量子力学导论》)
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