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Say I have a system with a spatial part and a spin degree of freedom, hence the wavefunction generally looks like [itex]\psi_+(\textbf r) |+\rangle + \psi_-(\textbf r) |- \rangle[/itex] w.r.t. for example the z-axis.

Now what if I'm simply interested in the spatial part? Can I perform an operation on this wavefunction such that I get a new wavefunction that is only spatial, but gives the same predictions for any observable that only depends on space variables? (e.g. [itex]L_z[/itex])

I feel this must be possible, and that it shouldn't even be hard, but I can't seem to think of the appriopriate operation right away and I also can't google it because I don't know what such an operation would be called.

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# How can I ignore information in my wave function?

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