# Homework Help: Commutator relations

1. Feb 2, 2007

### alisa

given that [x,p]=ih, show that if x=x, p has the representation p=-iħ∂/∂x+f(x) where f(x) is an arbitrary function of x

2. Feb 3, 2007

### Tom Mattson

Staff Emeritus
alisa, you're supposed to show an attempted solution at the problem. That goes for your other threads as well.

What do you mean " if x=x". x=x by definition.

3. Feb 3, 2007

### dextercioby

It's the coordinate representation in which the Hilbert space is $L^{2}(\mathbb{R},dx)$. The "x" operator is realized by a multiplication by "x". She's asked to prove that the most general representation of the momentum operator in this Hilbert space is the one written there.

4. Feb 3, 2007

### Tom Mattson

Staff Emeritus
OK, so then it should read something like "If $\hat{x}|\psi>=x|\psi>$...", right?

Last edited: Feb 3, 2007
5. Feb 3, 2007

### dextercioby

Exactly. That's the spectral equation, but nonetheless, yes.