- #1
spacetimedude
- 88
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Homework Statement
Deduece the commutation relations of position operator (squared) [itex]\hat R^2[/itex] with angular momentum [itex]\hat L[/itex]
Homework Equations
[xi,xj]=0, Lj= εijkxjPk, [xi, Pl]=ih, [xi,Lj]=iℏϵijkxk
The Attempt at a Solution
The previous question related R and L and the result was [tex][\hat R,\hat L_j]=i \hbar \epsilon _{ijk}x_k[/tex] after setting up the commutator as [tex]\epsilon _{jkl}[x_i,x_kP_l][/tex] where I did not include the i in the epsilon.
Now, I did the same with with [itex][\hat R^2,\hat L_j][/itex] and set it up as [tex][\hat R^2,\hat L_j]=[x_ix_i,L_j]=\epsilon_{jkl}[x_i,P_l]x_kx_i+x_i\epsilon_{jkl}[x_i,P_l]x_k[/tex], in which I simplified using the commutator property, and which is then equal to [tex]i\hbar\epsilon_{jkl}x_kx_i+i\hbar x_i\epsilon_{jkl}x_k[/tex]. I don't think I can reduce it any further.
The solution has the i included in the epsilon in the setup and I don't know why that is.
Any help will be appreciated