算符毕竟不是常矢量

Viktor posted @ Mar 28, 2008 10:59:03 AM in 有关物理的小零碎 with tags 物理 量子力学 算符 点乘 叉乘 , 3443 阅读

因而没办法满足平常的点乘和叉乘。算符的点乘与叉乘是这样定义的:

{\mathbf{\^A}}\cdot{\mathbf{\^B}}=\sum_\alpha A_\alpha B_\alpha

(\mathbf{\^A}\times\mathbf{\^B})_\gamma=\sum_{\alpha\beta\gamma}\epsilon_{\alpha\beta\gamma}A_\alpha B_\beta

可见这两个运算的性质相当差,点乘不能交换,叉乘不能反交换。

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