As I understand it, the magnitude of an [itex] L_z [/itex] eigenfunction's value is independent of its argument's [itex] \phi [/itex] coordinate (the longitude). Or, to paraphrase Richard L. Liboff (section 9.3 of Introductory Quantum Mechanics), when a system is in an eigenstate of [itex] L_z, | Y _{l} ^{m} | [/itex] is rotationally symmetric about the z axis.(adsbygoogle = window.adsbygoogle || []).push({});

So then, if I perform an [itex] L_z [/itex] measurement on a particle which is near the origin of some spherical coordinate system and its state changes to an [itex] L_z [/itex] eigenstate, and then I immediately perform a position measurement, the probability of finding it with any particular [itex] \phi [/itex] coordinate (plus or minus whatever [itex] \phi [/itex] angle you choose) is the same.

But what if the particle's original location is very far from the origin, or if it's very massive, or both? Could performing a quantum mechanical observation cause it move all the way to the other side of the origin, for example?

This question seems like it has something to do with the correspondence principle - or perhaps the apparent violation of it - but I cannot quite see it through.

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# About measuring angular momentum

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