- #1

happyparticle

- 369

- 19

- Homework Statement:
- Find Clebsch-Gordan coefficients ##\langle j,1;m,0| j',m' \rangle##

- Relevant Equations:
- ##\langle j,1;m,0| j',m' \rangle##

Hi,

I spent the entire day trying to figure out how to find the Clebsch-Gordan coefficients.

For example, if I have something like ##\langle 1,1;2,0|2,1 \rangle## I know how to find it in a table.

However, here I have ##\langle j,1;m,0| j',m' \rangle##

I found that ##\langle j,1;m,0| j',m' \rangle = \frac{m}{\sqrt{j(j+1)}}##, but I have no idea how they get it. They just throw this answer without explanation.

Edit: while looking for explanation on the internet I found the same homework that I'm trying to do, but this time there is a in-between problem with this hint : ## |j,j \rangle = ( \sqrt{j} |j,1;j,0 \rangle - | j,1; j-1,1 \rangle)##

So I'm guessing that with this hint and ##\langle j,1;m,0| j',m' \rangle## I could find what I'm looking for, but I'm not sure how and I don't even know how to get ## |j,j \rangle = ( \sqrt{j} |j,1;j,0 \rangle - | j,1; j-1,1 \rangle)##

Thank you

I spent the entire day trying to figure out how to find the Clebsch-Gordan coefficients.

For example, if I have something like ##\langle 1,1;2,0|2,1 \rangle## I know how to find it in a table.

However, here I have ##\langle j,1;m,0| j',m' \rangle##

I found that ##\langle j,1;m,0| j',m' \rangle = \frac{m}{\sqrt{j(j+1)}}##, but I have no idea how they get it. They just throw this answer without explanation.

Edit: while looking for explanation on the internet I found the same homework that I'm trying to do, but this time there is a in-between problem with this hint : ## |j,j \rangle = ( \sqrt{j} |j,1;j,0 \rangle - | j,1; j-1,1 \rangle)##

So I'm guessing that with this hint and ##\langle j,1;m,0| j',m' \rangle## I could find what I'm looking for, but I'm not sure how and I don't even know how to get ## |j,j \rangle = ( \sqrt{j} |j,1;j,0 \rangle - | j,1; j-1,1 \rangle)##

Thank you

Last edited: