Consider a spin 1/2 particle of magnetic moment M=yS. The spin state space is spanned by the basis of the | - > vectors, eigenvectors of S with eigenvalues + h/2 and -h/2. At time r=-, the state of the system is seen in attached file as well as questions a,b, and c.
Reference: "Cohen Quantum Mechanics"
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The solution is attached below in ...
The solution shows, in detail, how to utilize the basis transformation matrix in order to convert from one basis to another which simplifies the solution. It also calculates the time evolution of the wave function and the probabilities associated with the spin observables.