# Stern-Gerlach Experimental Calculation

1. Apr 22, 2008

### SharkyDx

I've run into a problem which has been bugging me for days. I know its related to the Stern-Gerlach experiment about firing hydrogen through an inhomogeneous magnetic field, but all i can do is give a vague qualitative description of the answers, and not an actual numerical one (because I don't entirely know what equations should be useful).

I know theres stuff about magnetic moments and spin and dipole moments happening here, but I can't seem to reconcile all these ideas. I'm not looking for a raw solution (I still want to learn something), just pointers as to the physics that's happening here, and possibly what equations are useful. Thanks.

I know (basically) that because of the inhomogeneous magnetic field, the atoms experience a force in the z-direction (vertically). Classically, theres stuff about all possible ranges of spin/momentum (or something) which would give a continuous band on the screen. Quantum mechanically, theres stuff about quantized spins that will only allow discrete outcomes, and i think the relativistic bit refers to the spin quantum number, m_s, but it might not. I can kinda handle the first three parts (if I'm even on the right track), but the fourth part - actually finding where the beam will appear - is a bit mysterious at the moment.

Thanks again.

2. Apr 22, 2008

### olgranpappy

check out the very first chapter of Sakurai's "Modern Quantum Mechanics"--it's about the S.G. experiment.

3. Apr 23, 2008

### pam

For 4, use the equation for the force on a dipole $$F=(\mu\cdot\nabla)B$$,
wilth spin up and spin down.