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]).(adsbygoogle = window.adsbygoogle || []).push({});

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,

AB

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# Formalism and Angular Momentum Expectation Values

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