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Zero uncertainity in components of angular momentum in Hydrogen atom

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up vote 6 down vote favorite 1 It is given that L and Lz,Lx,Ly commute.(L is total angular momentum, Lx is angular momentum along x axis). So, I can simultaneously know the value of let's say L and Lz. But, if I perform huge no of measurements and in a certain measurement, I get the value of L = Lz, then I know for certain that Lx and Ly are 0. But, according to the uncertainty principle, I can't know the exact values of any two of Lx, Ly and Lz. So, where did I go wrong? quantum-mechanics angular-momentum atomic-physics quantum-spin heisenberg-uncertainty-principle share | cite | improve this question asked Nov 24 at 13:47 ...