1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Commutation relation of R^2 with L

  1. Nov 2, 2016 #1
    1. The problem statement, all variables and given/known data
    Deduece the commutation relations of position operator (squared) [itex]\hat R^2[/itex] with angular momentum [itex]\hat L[/itex]

    2. Relevant equations
    [xi,xj]=0, Lj= εijkxjPk, [xi, Pl]=ih, [xi,Lj]=iℏϵijkxk

    3. 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
     
  2. jcsd
  3. Nov 2, 2016 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I can't follow your use of the epsilon symbol. Why not try calculating:

    ##[x^2, p_x]##

    And from there:

    ##[R^2, L_x]##

    Before you do the calculation, though, what do you think the answer will be?
     
    Last edited: Nov 2, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Commutation relation of R^2 with L
Loading...