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I'm trying Tripos question

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?

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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?

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