Please see attached for full question.
A particle of spin 1/2 is placed into a magnetic field with a Hamiltonian of (see attachment)
1. Find the eigenvalues and eigenvectors?
2. A particle is initially prepared to be in a state .... Find x(t)
3. If you measure the z-component of the particles angular momentum, what is the time dependent probability of finding - h/2 ?
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The solution is attached below in two files. the ...
The solution explains in detail how to find the energy levels and the eigenstates of the system, How an initial state evolves in time in terms of the eigenstates and finally how to calculate the probability to measure spin down as a function of time.