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]

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

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.