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

Show that: [p,x] = -iħ,

Show that: [p,x^n] = -niħ x^(n-1), n>1

Show that: [p, A] = -iħ dA/dx

Where p = -iħ d/dx, and A = A(x) is a differentiable function of x.

2. Relevant equations

[p,x] = px - xp;

3. The attempt at a solution

So far I understand part of each of these, to begin with the first part:

[p,x] = [(-iħ d/dx) (x)] - [(x) (-iħ d/dx)]

- From this, I simply get -iħ on the left hand side, which is already my answer that I'm looking for, but I do not understand how the right hand side simply cancels out or goes away, maybe I'm mistaken in my understanding of commutators?

For the 2nd part, I as well have -niħ x^(n-1) on the left, yet again what my goal is, and thus same problem with right hand side... Any assistance in this would be greatly appreciated, thank you.

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# Show that: Commutator relations (QM)

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