What Are the Properties of the Commutator in the Dilation Operator?

[Keyoke]

Homework Statement

Concicer the dilation operator

$D = \vec{r} * \vec{p}$

Compute $[D,\vec{r} ] and [D, \vec{p}]$

Homework Equations

$p = - i * hbar$

The Attempt at a Solution

I think the question is really if $[D, \vec{r}]$ commutes

I got this:
$D = \vec{r} * \vec{p}$
$D = x p_x + y p_y + z p_z$


for the x direction:

$[D, r] = [D, x] = [x, x p_x]$

where do i take it from here?

 

[dextercioby]

You have absolutely no idea ?? Pick up your book and find those brackets (called <commutator>) and the properties they have.