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Angular Momentum Operator.

  1. Nov 18, 2011 #1
    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.
     
  2. jcsd
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