# Matrix Elements

## Homework Statement

Does anyone know what the formula is for the following:

<j m | S^2_+ |j m > = ?

Reference to equations in Sakurai would be helpful in deriving the relation. I would suspect 3.5.37 but what about the delta_j j' ?

## Answers and Replies

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3.5.35 a

<j',m|J^2 |j,m> = j(j+1)hbar^2 delta_j j' delta m m'

3.5.37 is

J_+ |j,m> = c_jm^+ |j,m+1>

gabbagabbahey
Homework Helper
Gold Member
Well, I'd start by calculating $S_{-}|j,m\rangle$...what do you get for that?

J_- |j,m> = c_{j,m}^+ |j,m-1>

The formula that i'm interested in is :
<j m | S^2_+ |j m > = delta_m',m+2 c_jm^+ c_j m+1 ^+

But I don't understand how that is constructed, it's not in sakurai.

gabbagabbahey
Homework Helper
Gold Member
Well, $\langle j,m|S^2_{-}|j,m\rangle=\langle j,m|(S^2_{-}|j,m\rangle)$ and $S^2_{-}|j,m\rangle=S_{-}(S_{-}|j,m\rangle)=$___?

ok thx

Well, $\langle j,m|S^2_{-}|j,m\rangle=\langle j,m|(S^2_{-}|j,m\rangle)$ and $S^2_{-}|j,m\rangle=S_{-}(S_{-}|j,m\rangle)=$___?
Normally J_+*J_- is substituted as J^2 - J_z^2+hbarJ_z

As you described above, J_+(J_-J_+), wouldn't the content in parenthesese just cancel out?