(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using matrix representations find [itex]L^{3}_{x},L^{3}_{y},L^{3}_{z}[/itex] and from these show that [itex]L_{x},L_{y},L_{z}[/itex] 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

[tex]L_z=\hbar \left( \begin{array}{ccc}

1 & 0 & 0 \\

0 & 0 & 0 \\

0 & 0 & -1 \end{array} \right)[/tex]

But I've never before come upon reference to [itex]L^{3}_{x},L^{3}_{y},L^{3}_{z}[/itex]; what would matrix representations for these look like? Then there's the question about finding the roots of the algebraic equation; when talking about [itex]L_x[/itex] I would tend to think of [itex]L_x=yp_z-zp_y[/itex] as being the algebraic equations. If I'm correct then there is some analog for [itex]L^{3}_{x}[/itex]? How does that flow from the matrix representation?

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

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# Homework Help: Angular Momentum Operator.

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