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Introduction

and triplet states are given as: | χ s = 1, m = 0 ⟩ = 1 2 (| ↑ ⟩ | ↓ ⟩ + | ↓ ⟩ | ↑ ⟩); | χ s = 1, m = 1 ⟩ = | ↑ ⟩ | ↑ ⟩; | χ s = 1, m = − 1 ⟩ = | ↓ ⟩ | ↓ ⟩. {\displaystyle {\begin{aligned}&|\chi _{s=1,m=0}\rangle ={\frac {1}{\sqrt {2}}}(|\uparrow \rangle |\downarrow \rangle +|\downarrow \rangle |\uparrow \rangle)\;;\\&|\chi _{s=1,m=1}\rangle =\;|\uparrow \rangle |\uparrow \rangle \;;\;\;|\chi _{s=1,m=-1}\rangle =\;|\downarrow \rangle |\downarrow \rangle \;.\end{aligned}}} ψ (r 1, r 2) = − ψ (r 2, r 1) {\displaystyle \psi (\mathbf {r} _{1},\mathbf {r} _{2})=-\psi (\mathbf {r} _{2}\,,\mathbf {r} _{1})}