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The operators representing the components of angular momentum are incompatible, since

[tex][L_x,L_y] = i\hslash L_z [/tex].

If you apply the uncertainty principle to this you get:

[tex]\sigma_{L_x}\sigma_{L_y} \geq \tfrac{\hslash}2|\langle L_z \rangle|[/tex].

But what if [tex]\langle L_z \rangle = 0[/tex]? Then the HUT does not prevent simultanoeus eigenstates of Lx and Ly or what?

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# Angular momentum and the HUT

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