# Eigenvalues and eigenvectors of J.n

1. Jan 19, 2012

### dfschick

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. Jan 20, 2012

### vela

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