- #1

Kara386

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## Homework Statement

Using the commutation relations ##[x,p_x] = i\hbar## etc, together with the ##SO(3)## generators ##J_k (k=x,y,z)## in their operator form to calculate ##[J_x, \mathbf{r}]## and ##[J_x, \mathbf{p}]## where ##r = (x, y, z)## and ##p = (p_x, p_y, p_z)##.

Then show that ##[J_k, r^2]=0##.

## Homework Equations

## The Attempt at a Solution

I can't find the operator forms anywhere. I have looked on the internet and in textbooks, but nowhere does it specifically state that a particular form is the 'operator' form. Is it just these matrices:

##

\left( \begin{array}{ccc}

0& 0 & 0 \\

0& 0 & 1 \\

0& -1 & 0 \end{array} \right) ##

##

\left( \begin{array}{ccc}

0& 0 & -1 \\

0& 0 & 0 \\

1& & 0 \end{array} \right) ##

##

\left( \begin{array}{ccc}

0& 1 & 0 \\

-1& 0 & 0 \\

0& 0 & 0 \end{array} \right) ##

Even if that's the case how could I show ##[J_k, r^2]=0##? ##J_k## could be anyone of the three. Do I have to show it for all of them?

Any help is much appreciated!

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