- #1
rogeralms
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Homework Statement
Let A and B be two observables that both commute with their commutator [A,B].
a) Show, e.g., by induction, that [A,Bn]=nBn-1 [A,B].
The Attempt at a Solution
Prove for n=1
[A,B1]=1B1-1 [A,B].
[A,B]=B0[A,B]=[A,B]
Show that it is true for n+1
[A,Bn+1]=[A,BnB]=Bn[A,B]+[A,Bn]B
I am not sure how to continue. Could someone give me a hint what I should do next?
Thank you.