Eigenvalues and eigenvectors of J.n

[dfschick]

Homework Statement

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.

Homework Equations

Matrix representations for J^2 and J(z)

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.

 

[vela]

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