[A,BC] = [A,B]C + B[A,C]

This commutator product rule works just like the differentiation product rule:

assume that A is independent of C, you get the first term;

assume that A is independent of B, you get the second term.

— Me@2012-03-27 7:24:30 PM

2012.03.31 Saturday (c) All rights reserved by ACHK