Why do we choose a quantization axis for angular momentum?

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matematikuvol
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What is quantisation axis? In many books authors just say that we choose that z is quantization axis.
 
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This is just saying that you consider everything in a basis, where the [itez]z[/itex] components of angular momenta have well-determined values (eigenstates of the corresponding [itex]\hat{J}_z[/itex] operators).