1. The problem statement, all variables and given/known data Using (x,p) = i (where x and p are operators and the parentheses around these operators signal a commutator), show that: a)(x^2,p)=2ix AND (x,p^2)=2ip b) (x,p^n)= ixp^(n-1), using your previous result c)evaluate (e^ix,p) 2. Relevant equations For operators, in general: (ab,c)=a(b,c)+(a,c)b (a,bc)=(a,b)c + b(a,c) 3. The attempt at a solution I have no trouble showing (a): (x^2,p)=x(x,p)+(x,p)x=x(i) + i(x)=2ix Same general strategy for (x,p^2) In (b), I get lost when trying to apply the result I have already found. My attempt: (x,p^n)=(x,p*p^(n-1)=(x,p)p^(n-1)+p(x,p^(n-1))=ip^(n-1) + p(x,p^(n-1)) I don't know where to go from here. I have tried pulling out more factors of p from the second term, but that gets me no where (at least from what I can see). I have also just played around a lot with the commutator, even starting from the end: ixp^(n-1)=(x,p)p^(n-1)= xp^n - pxp^(n-1), but again, after this, whichever path I take doesn't seem to be fruitful. Thanks!