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Classical Angular Momentum 
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#1
Jan113, 03:44 PM

P: 15

[L_{i},L_{j}]=ε_{ijk}L_{k}
how can I prove this expression classically? 


#2
Jan113, 04:29 PM

Sci Advisor
P: 2,470

Classically, L is not an operator, so you cannot define a commutator.
You can show that {L_{i}, L_{j}}=ε_{ijk}L_{k}. I don't know if that's what you meant by saying "Classically". If so, just write out L_{i} in terms of q_{i} and p_{i}. If you write the correct expression for it using LeviCivita symbol and apply definition of Poisson bracket, it should be a trivial matter. 


#3
Jan213, 02:04 PM

P: 15

Yes, exactly. Thank you very much. Using square brackets may be confusing in classical mechanics. I figured out to make this with levi civita symbol. But there is another problem I have now. if I replace the L_{i} with some general vector V_{i}, it should still be hold
{V_{i},L_{j}}=ε_{ijk}V_{k} how should I constract a general V vector? 


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