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: Show that the expectation value of angular momentum <Lx> is zero

  1. Nov 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that the expectation value of angular momentum <Lx> is zero

    2. Relevant equations

    L±|l,m⟩ = SQRT(l(l+1)−m(m±1)h|l,m±1⟩

    L± = Lx ± iLy

    3. The attempt at a solution

    I'm supposed to use ladder operators here to show <Lx> is zero.

    I start with <Lx>=<l,m|Lx|l,m> but don't know where to go from here. I've tried different things but all the methods I've tried seem to lead to a dead end...
  2. jcsd
  3. Nov 19, 2011 #2
    Solve your second equation to get [itex]L_x[/itex] in term of [itex]L_+[/itex] and [itex]L_-[/itex].

    Now, substitute this [itex]L_x[/itex] in to [itex]\langle L_x \rangle[/itex] and use the first equation to calculate it.
  4. Nov 19, 2011 #3
    I'm not seeing how that would help. Then I just get an equation in terms of L+, L- and Ly.

    Lx=L± minus plus iLy
  5. Nov 20, 2011 #4
    Can anyone help me out here?
  6. Nov 20, 2011 #5
    Use what mathfeel said and think about orthogonality of |l,m> states.
  7. Nov 20, 2011 #6


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You have two equations:
    \hat{L}_+ &= \hat{L}_x + i\hat{L}_y \\
    \hat{L}_- &= \hat{L}_x - i\hat{L}_y
    \end{align*}Solve them for Lx in terms of L+ and L-.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook