Quantum Mechanics Commutation Problem

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The discussion centers on demonstrating the commutation relation [Li, Lj] = ih εijk Lk using the Levi-Civita symbol. Participants suggest starting with the definitions of angular momentum operators and substituting them into the commutation bracket. The properties of the Levi-Civita symbol are highlighted, noting that it equals 1 for cyclic indices, -1 for anticyclic indices, and 0 otherwise. The problem is considered straightforward, with an emphasis on applying these definitions correctly. Understanding these concepts is crucial for solving the commutation problem in quantum mechanics.
metkar
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[Li, Lj]=ih εijk Lk
the problem is , show that this equation.Can you help me to solve this problem with levi-civita symbol?
 
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its really not very tricky. start off by definitions of the angular momentum operators. substitute and do the bracket. the levi-civita symbol has a common definition which ucan find in all textbooks. if ijk are in cyclic order then the epsilon is equal to 1. if they are in anticyclic order like kji then the epsilon is -1. any other cases results in epsilon = 0
 
thanks for your help
 

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