# Stern-Gerlach confusion

1. Apr 26, 2008

### Rory9

1. The problem statement, all variables and given/known data

Consider a beam of spin-(1/2) particles passed through a Stern-Gerlach apparatus (+ve z orientation).

The particles are in the ground-state of the Hamiltonian

$$H = \frac{g\mu_{B}\hbar}{2} \left( ^{B_{z}}_{ B_{x} + iB_{y} }^{ B_{x} - iB_{y}}_{ - B_{z} } \right)$$

and therefore aligned with the field B. For an incident beam intensity of 1, calculate the intensity of the transmitted beam(s).

3. The attempt at a solution

I'm honestly not sure what to do with this. I can compute the eigenvectors of the Hamiltonian (Bz + B,Bx + iBy) & (Bz - B,Bx + iBy), and deduce the ground state from the one whose eigenvalues gives the lowest energy (I presume), but what then?