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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


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    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.
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