# Angular Momentum Operator.

1. Nov 18, 2011

### atomicpedals

1. The problem statement, all variables and given/known data

Using matrix representations find $L^{3}_{x},L^{3}_{y},L^{3}_{z}$ and from these show that $L_{x},L_{y},L_{z}$ satisfy the same algebraic equations. What are the roots of the algebraic equations?

2. The attempt at a solution

My problem is that I'm not sure what this question is asking me. I know what matrix reprsentations are; for example

$$L_z=\hbar \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & -1 \end{array} \right)$$
But I've never before come upon reference to $L^{3}_{x},L^{3}_{y},L^{3}_{z}$; what would matrix representations for these look like? Then there's the question about finding the roots of the algebraic equation; when talking about $L_x$ I would tend to think of $L_x=yp_z-zp_y$ as being the algebraic equations. If I'm correct then there is some analog for $L^{3}_{x}$? How does that flow from the matrix representation?

I'm horribly confused here, any help is greatly appreciated.