Is it possible measure simultaneously square of angular momentum and its x projection ( ^L2 and ^Lx )?Why? Proof.

Question

Is it possible measure simultaneously square of angular momentum and its x projection ( ^L2 and ^Lx )?Why? Proof.
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Solution 1

Yes, it is possible to simultaneously measure the square of the angular momentum and its x projection. This is because the operators corresponding to these two quantities commute, meaning that the order in which they are applied does not affect the result.

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