Is it correct to write for the uncertainty $$\Delta \vec L=\Delta L_x+\Delta L_y+\Delta L_z$$ meaning $L$ is the angular momentum and $L_x,L_y,L_z$ the components. I couldn't find an answer in my textbooks.
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$\begingroup$ Left hand side is a vector triplet. Right hand side is only one number? $\endgroup$– Cosmas ZachosCommented Apr 17, 2018 at 19:08
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$\begingroup$ That was my first thought also...but it was in the question of the exercise, find the uncertainty for $\vec L$..strange..i have to talk to my teacher. $\endgroup$– AnastasiosCommented Apr 17, 2018 at 20:35
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$\begingroup$ Κύριε Ζάχο, τιμή μου που αφιερώσατε το χρόνο σας σε μια τέτοια ερώτηση..Σας ευχαριστώ! $\endgroup$– AnastasiosCommented Apr 17, 2018 at 20:44
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It doesn't really make sense to talk about the vector $\vec L$ in QM because we know from the uncertainty principal that we can only know about one component of the momentum as well as the magnitude of the momentum ($L^2$). Since we can simultaneously diagonalize a component (say $L_z$) and the magnitude, we can talk about the uncertainty in each by calculating the expectation values as we usually would for an operator.
If you want to talk about the uncertainty of $L$, it makes more sense to talk about the uncertainty in the scalar quantity $\sqrt{L^2}$, the operator that represents the magnitude of the momentum.
