I'm having trouble figuring out the following commutator relation problem:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose A and B commute with their commutator, i.e., [tex][B,[A,B]]=[A,[A,B]]=0[/tex]. Show that

[tex][A,B^{n}]=nB^{n-1}[A,B][/tex]

I have

[tex][A,B^{n}] = AB^{n} - B^{n}A[/tex]

and also

[tex][A,B^{n}] = AB^{n} - B^{n}A = ABB^{n-1} - BB^{n-1}A[/tex]

I don't know where to go from here. I'm not positive the above relation is correct either.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Show that [A,B^{n}]=nB^{n-1}[A,B]

**Physics Forums | Science Articles, Homework Help, Discussion**