- #1

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## 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' ?

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- Thread starter Nusc
- Start date

- #1

- 753

- 2

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' ?

- #2

- 753

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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>

<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>

- #3

gabbagabbahey

Homework Helper

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Well, I'd start by calculating [itex]S_{-}|j,m\rangle[/itex]...what do you get for that?

- #4

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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.

- #5

gabbagabbahey

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- #6

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ok thx

- #7

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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?

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