Calculate [D, r] and [D, p] with Dilatation Operator

[Goodwater]

Homework Statement

Consider the dilatation operator: D = r * p

Calculate [D , r] and [D , p]

Homework Equations

The Attempt at a Solution

 

[arkajad]

It is not clear what r stand for and what * stands for. Do you mean

$$D=\mathbf{r}\cdot\mathbf{p}=xp_x+yp_y+zp_z$$?

Do you mean $[D,\mathbf{r}]$ or $[D,r]$ where $r=\sqrt{\mathbf{r}^2}$. These details are important.

 

[Goodwater]

Hi.

Thank you for reply.

You are correct: D = xpx + ypy + zpz
I meant [D,r] where r is not square root.

I hope this is more understandable, as this is my first post I don't know how to get the notations right:)

 

[arkajad]

The you calculate using $[AB,C]=A[B,C]+[A,C]B$, for isntance

$$[xp_x,x]=x[p_x,x]+[x,x]p_x=\ldots$$

Mostly you will get zeros, but occasionally you will get a term that will contribute.