1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Commutator relations

  1. Jan 16, 2014 #1
    I'm doing something horribly wrong in something that should be very easy. I want to show that:

    [itex][L^2, x^2] = 0[/itex]


    [itex][L^2, x x] = [L^2, x] x + x [L^2, x][/itex]

    [itex]L^2 = L_x^2 + L_y^2 + L_z^2[/itex]

    Therefore: [itex][L^2, x] = [L_x^2 + L_y^2 + L_z^2, x] = [L_x^2, x] + [L_y^2, x] + [L_z^2, x][/itex]

    = [itex]L_y [L_y, x] + [L_y, x] L_y + L_z [L_z, x] + [L_z, x] L_z[/itex]

    [itex]= -i h L_y z - ih z L_y + i h L_z y + i h y L_z[/itex]


    [itex][L^2, x x] = -i h L_y z x - ih z L_y x + i h L_z y x + i h y L_z x
    + -i h x L_y z - ih x z L_y + i h x L_z y + i h x y L_z[/itex]

    And now?

    This ought to be a lot easier.
  2. jcsd
  3. Jan 16, 2014 #2


    User Avatar
    Science Advisor

    Where did this exercise come from? I suspect you misunderstand what ##x^2## means here, but I can't be sure without seeing the original unedited question.

    (BTW, you're supposed to use the homework template when posting in this forum -- else you risk attracting the Wrath of the Mentors.)
  4. Jan 16, 2014 #3
    Ughy. You are right. I looked it up again and it's not actually x^2 as in "position operator squared" but X^2 = x^2 + y^2 + z^2.

    I didn't sleep for 29 hours now, working for some exams. I'm slightly confused. My bad. Next time I'll use the exact template. :redface:
  5. Jan 16, 2014 #4


    User Avatar
    Science Advisor

    This is a really bad technique. You are probably more confused than you realize, maybe even approaching a delirium state. Non-sleeping is counter-productive. Things that take ages to understand or perform while tired tend to be much quicker when you're fresh.

    Go and sleep (even if just for a few hours -- set the alarm clock accordingly).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted