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Classical Angular Momentum

by ssamsymn
Tags: angular, classical, momentum
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ssamsymn
#1
Jan1-13, 03:44 PM
P: 15
[Li,Lj]=εijkLk

how can I prove this expression classically?
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K^2
#2
Jan1-13, 04:29 PM
Sci Advisor
P: 2,470
Classically, L is not an operator, so you cannot define a commutator.

You can show that {Li, Lj}=εijkLk. I don't know if that's what you meant by saying "Classically". If so, just write out Li in terms of qi and pi. If you write the correct expression for it using Levi-Civita symbol and apply definition of Poisson bracket, it should be a trivial matter.
ssamsymn
#3
Jan2-13, 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 Li with some general vector Vi, it should still be hold

{Vi,Lj}=εijkVk

how should I constract a general V vector?


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