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单词 Exchange operator
释义

Exchange operator

中文百科

交换算符

交换算符(英语:Exchange Operator)是一种量子力学算符,作用于多粒子量子系统。

交换算符的定义如下:

 \hat {P_{12}}|a,b\rangle = |b,a\rangle

其中, \hat P_{12} 即为交换算符。其作用为,将系统中两个粒子所处的态交换。在上面的例子中,态 |a,b\rangle 变换成为 |b,a\rangle 。显然,对同一个系统做两次交换可以得到原系统。假设交换算符的本征值为 \alpha ,则

 {\hat P_{12}}^2|a,b\rangle = \hat P_{12}\alpha|b,a\rangle = \alpha\hat P_{12}|b,a\rangle = \alpha^2|a,b\rangle

所以, \alpha = \pm1 。由此得到交换算符是自伴算子且是幺正算符。

英语百科

Exchange operator 交换算符

Anticlockwise rotationClockwise rotationExchange of two particles in 2 + 1 spacetime by rotation. The rotations are inequivalent, since one cannot be deformed into the other (without the worldlines leaving the plane, an impossibility in 2d space).

In quantum mechanics, the exchange operator \hat{P} is a quantum mechanical operator that acts on states in Fock space. The exchange operator acts by switching the labels on any two identical particles described by the joint position quantum state \left|x_1, x_2\right\rangle. Since the particles are identical, the notion of exchange symmetry requires that the exchange operator be unitary.

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更新时间:2025/6/24 0:18:08