- #1
brooke1525
- 15
- 0
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,
AB
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