- #1

- 13

- 0

## Homework Statement

I am supposed to find if the following commutes: [L

_{x},L

_{y}]

## Homework Equations

L

_{x}= -i[tex]\hbar[/tex][y([tex]\partial/[/tex][tex]\partial[/tex]z) - z([tex]\partial/[/tex][tex]\partial[/tex]y)]

L

_{y}= -i[tex]\hbar[/tex][z([tex]\partial/[/tex][tex]\partial[/tex]x) - x([tex]\partial/[/tex][tex]\partial[/tex]z)]

where [L

_{x},L

_{y}]=L

_{x}L

_{y}-L

_{y}L

_{x}

If it commutes then [L

_{x},L

_{y}]=0

## The Attempt at a Solution

[L

_{x},L

_{y}]= (i[tex]\hbar[/tex])

^{2}{[y([tex]\partial/[/tex][tex]\partial[/tex]z) - z([tex]\partial/[/tex][tex]\partial[/tex]y)[z([tex]\partial/[/tex][tex]\partial[/tex]x) - x([tex]\partial/[/tex][tex]\partial[/tex]z)]}

After expanding this I got a result of 0. So my solution concluded that they commute.

The answer however is [L

_{x},L

_{y}]= i[tex]\hbar[/tex]L

_{x}

I clearly expanded it wrong. I was hoping if anyone could explain how they expanded the L

_{x}L

_{y}-L

_{y}L

_{x}part. In my calculations I cannot seem to figure out how the answer contains a few more parts in the expansion which results in a non-commutation..

Thanks!