How to Derive Isospin States in Particle Physics?

[dunk]

Homework Statement

Particle Physics- Isospin states

Relevant Equations

$$\arrowvert 2, 2\rangle=\arrowvert 1,1\rangle \otimes \arrowvert 1,1\rangle$$
$$ \langle 1,1 \arrowvert2,1 \rangle=0$$

Hi, I have attached the question to this post. I understand on the process on getting to the answer in that you use $$\arrowvert 2, 2\rangle=\arrowvert 1,1\rangle \otimes \arrowvert 1,1\rangle$$ and apply the isospin-lowering operator to obtain $$\arrowvert 2,1 \rangle$$. Then I understand you then use orthogonality $$ \langle 1,1 \arrowvert2,1 \rangle=0$$ to obtain the composition of $$\arrowvert 1,1 \rangle= (\langle 1,1 \arrowvert)^{\dagger} $$. But I'm unsure on how to actually get to each step and I'm not sure on where to go from this point. Any help will be much appreciated.

 

[vela]

This procedure should be covered in your quantum mechanics textbook in the chapter on angular momentum. Start there.