Quantum Mechanics Commutation Problem

[metkar]

[L_i, L_j]=ih ε_ijk L_k
the problem is , show that this equation.Can you help me to solve this problem with levi-civita symbol?

 

[ardie]

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

 

[metkar]

thanks for your help