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Homework Help: Eigenvalues and eigenvectors of J.n

  1. Jan 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Calculate the eigenvalues and eigenvectors of the operator, J.n, where n is a unit vector characterized by the polar angles theta and phi, and J is the spin-1 angular momentum operator.

    2. Relevant equations
    Matrix representations for J^2 and J(z)

    3. The attempt at a solution
    I think that the first step is to develop the matrix for J.n but I'm not sure how that relates to the other matrices.
  2. jcsd
  3. Jan 20, 2012 #2


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    You want to use ##\hat{\vec{J}}\cdot\mathbf{\hat{n}} = \hat{J}_x n_x + \hat{J}_y n_y + \hat{J}_z n_z##.
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