- #1
Don'tKnowMuch
- 21
- 0
Homework Statement
Calculate [P^m, X^n]
Homework Equations
[P,X] = PX - XP
The Attempt at a Solution
P( P^(m-1) * X^(n-1))X - (X^n)(P^n)
=(XP +[P, X])(P^(m-1)*X^(n-1)) - (X^n)(P^n)
=(P^m)(X^n) + [P, X](P^(m-1))(X^(n-1))- (X^n)(P^n)...
I don't think the direction i am taking will be helpful. Is there some other way to do this particular commutator? I know how to do [P, X^n], but my methods fail when P is raised to some power.