I am a beginning with rotors and spin. I am trying to understand how spins connects to rotors.
Say I have a wave function $\psi = e^{a+e_0e_1 b}$.
I wish to prove that this function has spin 1/2. How would I do it?
Do I apply a rotor $R(\theta)=e^{e_0e_1 \theta/2}$ to $\psi$ and note the angles $\theta$ where the sign of $\psi$ flips to $-\psi$.
$$ R(\theta)\psi=e^{a+e_0e_1(b+\theta/2)} $$
Then at $4\pi$ (2 turns) I get $R(4\pi)\psi=\psi$