# Calculating the expectation value of a spin operator in a uniform magnetic field

I'm trying

Usually for these types of questions, I'm used to the field being in a specific direction. For example, if the field was in the z direction, I could find this solution by checking

|< Sz, Q >|^2 where Q is the state vector at time t.

Does anyone know how to begin the approach to this case where the field isn't in some specific direction?

Hint: Calculate $$\textbf{n} \cdot \textbf{S}$$, then use your result to find the eigenspinors and their associated eigenvalues of your Hamiltonian. Remember that $$x = r\sin\theta\cos\phi$$, $$y = r\sin\theta\sin\phi$$, and $$z = \cos\theta$$. Then you can write down the general state $$|{\chi(t)}\rangle$$, and solve the TDSE. Can you take it from here?