# 清華物理94應數

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## 題目 编辑

1. (15%)
The commutator
$[B,A]= B A - A B = \lambda I$
of two $n \times n$ square matrices $A$ and $B$ is proportional to the identity matrix $I$.
Choose only one answer for each questions.
1. $[B, A^n]=?$(A)$0;$(B)$n;$(C)$n\lambda A^n;$(D)$n\lambda A^{n-1};$

## 參考解答 编辑

1. 主要觀念是對Commutation relation夠不夠熟悉
1. 當兩個operator/matrix的commutator為常數倍的identity時,
$[B, f(A)] = \lambda \frac{\partial f(A)}{\partial A}$