(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate [P^m, X^n]

2. Relevant equations

[P,X] = PX - XP

3. 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.

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# Homework Help: Compute commutator of [P^m, X^n]

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