Stern-Gerlach: Run Through X, Y & Z Axes?

[Hornbein]

The atoms go through a magnetic field aligned with the x axis. This separates the atoms into two groups, spin up and spin down. Run a group through such a field again and there is no change. Run a group through a field aligned with the z axis, you get two groups. Run one group through the x again and you get two groups.

What if this: The atoms go through a magnetic field aligned with the x axis. This separates the atoms into two groups, spin up and spin down. Run a group through a field aligned with the y axis, the third axis that is so far unused. Presumably this does not split the group, it simply accelerates it. Then run it through the x-axis field again. Does the group split into two?

 

[blue_leaf77]

Run a group through a field aligned with the y axis, the third axis that is so far unused. Presumably this does not split the group, it simply accelerates it.

Two groups will emerge out of this apparatus as it will for the case of magnetic field aligned in the other two axes and regardless in which direction in space the magnetic field is directed, it will always separate a 1/2-spin quantum object into two.