- #1

- 2

- 0

## Homework Statement

Show that

< l,m | L

_{x}

^{2}- L

_{y}

^{2}| l,m > = 0

## Homework Equations

L

^{2}= L

_{x}

^{2}+ L

_{y}

^{2}+ L

_{z}

^{2}

[ L

_{x}, L

_{y}] = i [STRIKE]h[/STRIKE] L

_{z}

[ L, L

_{z}] = i [STRIKE]h[/STRIKE] L

_{x}

[ L

_{z}, L

_{x}] = i [STRIKE]h[/STRIKE] L

_{y}

## The Attempt at a Solution

I tried substituting different commutation values in place of L

_{x}and L

_{y}, but I'm not reducing it any further. I also tried ladder operations, but my professor said they're not needed to solve the problem.