Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Formalism and Angular Momentum Expectation Values

  1. Nov 15, 2008 #1
    I seem to be having a rather difficult time understand all the details of the notation used in this quantum material. If I'm given the eigenvalue equations for L[tex]^{2}[/tex] and [tex]L_z[/tex] and [tex]L_{\stackrel{+}{-}}[/tex] for the state |[tex]\ell[/tex],m>, how do I compute <[tex]L_{x}[/tex]> using bra-ket formalism? I know that [tex]L_x[/tex] = (1/2)([tex]L_+[/tex] + [tex]L_-[/tex]).

    What I've got so far:

    Need to compute <[tex]\ell[/tex],m|[tex]L_x[/tex]|[tex]\ell[/tex],m>.

    = (1/2)(<[tex]\ell[/tex],m)([tex]L_+[/tex] + [tex]L_-[/tex])([tex]\ell[/tex],m>)


    Algebraically, what's the next step?

    Thanks in advance,
  2. jcsd
  3. Nov 16, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    [tex](1/2)\cdot (<l,m|L_+|l,m> +<l,m|L_-|l,m> ) = [/tex]

    the result should be pretty obious ;-)

    Anyway, this is general:

    Suppose we have, two operators A and B:

    <psi_i|(A+B)|psi_j> = <psi_i|A|psi_j> + <psi_i|B|psi_j>

    Next time you have homework related questions, ask them in the homework section.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook