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**1. Homework Statement**

My textbook takes a look at the [itex]\Delta(1232)[/itex] particle

It says that

[tex]\left|\pi p;\frac{3}{2},\frac{3}{2}\right>=\left|\pi;1,1\right>|N;\frac{1}{2},\frac{1}{2}\right>[/tex]

where N stands for a nucleon and pi could be any of the three flavours of pion.

They then go on by applying ladder operators (not explicitly, this is not at that level yet) to give

[tex] \left|\pi p;\frac{3}{2},\frac{3}{2}\right>=-\sqrt{\frac{1}{3}}\left|\pi^+ n\right>+\sqrt{\frac{2}{3}}\left|\pi^0 p\right>[/tex]

My question is how they came up with that

**2. Homework Equations**

Clebsch Gordon coefficients

For now use the wikipedia source but if you can suggest a better source please suggest it

http://en.wikipedia.org/wiki/Table_of_Clebsch-Gordan_coefficients

**3. The Attempt at a Solution**

Is the isospin of the pi+ is 1 and the isospin of the proton is 1/2?

in either case how did they come up with the coefficients of -root 1/3 and root 2/3??

the two spin values are j=1 and j=1/2. so we see two possiblities,

first is m=3/2

why is this possibility rejected?

the other possibility is where m=1/2

there are two possible j values. Look at the m1 values i could tell which woul the pi+/-/0 possibility. But the only way i would know if there was a neutron or proton would be to deduce it from the pion's spin and charge? Is that correct?

Also while reading the CG coefficients, is the j,m of the decaying particle, and then j1, and j2 of the products?

Thank you for all your help and advice!

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