Formalism and Angular Momentum Expectation Values

[brooke1525]

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^{2} and L_z and L_{\stackrel{+}{-}} for the state |\ell,m>, how do I compute <L_{x}> using bra-ket formalism? I know that L_x = (1/2)(L_+ + L_-).

What I've got so far:

Need to compute <\ell,m|L_x|\ell,m>.

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

=?

Algebraically, what's the next step?

Thanks in advance,
AB

 

[malawi_glenn]

(1/2)\cdot (&lt;l,m|L_+|l,m&gt; +&lt;l,m|L_-|l,m&gt; ) =

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.