Oh god, you're right thanks, this is embarassing... I got caught up in all of the minus' that are there and I went with it because of the i's in the ##\sigma_y## matrix. As for the proof I can think of one off the top of my head, which uses the commutativity of a hermitian operator (when doing...
So I was trying to see what the result for the spin precession would be if the magnetic field pointed in the y-direction instead of z. I feel like either something with what I'm doing is wrong or, I'm just overlooking something because I keep getting complex energy eigenvalues. So what I'm doing...