Hence, Equation (???) is explicitly symmetric: \[\begin{align} \begin{aligned} \hat{P}_{12} \, |+\!z, A\,;\, -z, B\rangle &= \frac{1}{\sqrt{2}} \Big(|\!-\!z\rangle|B\rangle |\!+\!z\rangle|...Hence, Equation (???) is explicitly symmetric: ˆP12|+z,A;−z,B⟩=1√2(|−z⟩|B⟩|+z⟩|A⟩+|+z⟩|A⟩|−z⟩|B⟩)=|+z,A;−z,B⟩. Likewise, if there is a spin-down particle at A and a spin-up particle at B, the bosonic two-particle state is \[|-\!z, A\,;\, +z, B\rangle = \frac{1}{\sqrt{2}} \Big…
