# Homework Help: Operator Theory Problem on Momentum Operator (QM)

1. Jun 29, 2013

### LolWolf

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

Given the operators $\hat{x}=x\cdot$ and $\hat{p}=-i\hbar \frac{d}{dx}$, prove that:

$[\hat{x}, g(\hat{p})]=i\hbar \frac{dg}{d\hat p}$

2. Relevant equations

None.

3. The attempt at a solution

I have very little idea on how to begin this problem, but I don't want a solution, I simply want a hint in the right direction.

Thanks, mates.

Last edited: Jun 29, 2013
2. Jun 29, 2013

### Dick

Expand $g(p)$ in a power series. What's $[x,p^n]$?

3. Jun 29, 2013

### LolWolf

Actually, I realized it was even easier than that, but thank you!

Consider the case in momentum-space rather than position-space, and this reduces nicely using elementary operations.

4. Jun 29, 2013

### Dick

Sure, that works also. x is a differentiation operator in p space.