1. The problem statement, all variables and given/known data 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]. 3. 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.