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To show that [ L^{2}, L_{+}] uses the following commutators [ L^{2}, L_{x}] = 0 and [ L^{2}, L_{y}] = 0 . But if [ L^{2}, L_{x}] = 0 this shows that L^{2}and L_{x}have simultaneous eigenstates ; but then should L^{2}and L_{y}not commute ?

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# I Angular momentum commutators

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