# Spin interaction with B field

1. Aug 15, 2013

### forceface

1. The problem statement, all variables and given/known data
The problem is stated on page 10 and it is number 9. http://panda.unm.edu/pandaweb/graduate/prelims/QM_F11.pdf

2. Relevant equations
I know how to write Sy in the z basis for either spin up or down and I have all the spinors.

3. The attempt at a solution
I tried solving for |ψ(t)> by using Bo as the hamiltonian but that seems to give me an answer that a is single solution and I was expecting a column vector as a solution. If I got a column vector I would just take the inner product of |<Sy|ψ(t)>|2 and that would give me the probability. With this said I feel like I am approaching this problem wrong and I have to take into account that fact that the magnetic field is in the z direction.

2. Aug 15, 2013

### Oxvillian

Hmm what you say above doesn't make much sense to me because $S_y$ and $H$ are supposed to be matrices.