Collapse of Wave: Effects on Energy & Position Measurements

[martinbn]

In the Stern-Gerlach experiment you cannot ignore position. It's the crucial point of this experiment that after running through the inhomogeneous magnetic field, you have a spin-position entangled state, namely
$$\psi^j(\vec{x})=\psi_{\text{left}}(\vec{x}) \chi_{\text{up}}^j + \psi_{\text{right}}(\vec{x}) \chi_{\text{down}}^j.$$
If you tailor your magnetic field right, the ##\psi_{\text{left}}## and ##\psi_{\text{right}}## functions peak practically in separated regions of space, and you can filter out one part by just blocking the corresponding partial beam of particles. Then you have prepared particles with a determined spin component in direction of the magnetic field, i.e., up or down.

The blocking is also due to the interactions of the particles with the medium used to block them. There's no other dynamics than quantum dynamics and no collapse hypothesis is necessary.

That's the same just more unnecessary details. The question remains. If the state, you wrote above, is the state of the atom before going through the SG apparatus, then the state after is only one of the summands. So there is some kind of collapse?