How many quantum numbers would the system have overall?

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uskalu
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If the angular momenta about three axes of rotation in a central potential did commute, how many quantum numbers would the
system have overall?
 
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If this is a homework question, it's not asked in the appropriate subforum. There's a subforum dedicated to HW questions.

I would like to help you find the answer to your question by yourself. That's why I'm asking you if you know other vector observable of a quantum system whose 3 components would commute among each other.