# 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?

I'd very much appreciate some helpful pointers! Thanks in advance.

(Also, perhaps there are some relevant examples somewhere online for this sort of problem?)

Last edited: Apr 26, 2008