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7.5: Electronic States of the H₂ Molecule
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/07%3A_Hydrogen_ion_and_Covalent_Bonding/7.05%3A_Electronic_states_of_the_H2_Molecule
This must be combined with a spin eigenfunction $\uparrow \uparrow$ , $\downarrow \downarrow$ , $(\uparrow \downarrow + \downarrow \uparrow )$ , or $(\uparrow \downarrow − \downarrow \uparrow )$ ...This must be combined with a spin eigenfunction $\uparrow \uparrow$ , $\downarrow \downarrow$ , $(\uparrow \downarrow + \downarrow \uparrow )$ , or $(\uparrow \downarrow − \downarrow \uparrow )$ , where the first arrow represents the spin state $(m_s = \pm 1)$ of the first electron. $\psi ({\bf r_1},{\bf r_2}, s_1, s_2) = [u^1_{100} ({\bf r_1}) + u^1_{100}({\bf r_2})][u^2_{100}({\bf r_1}) + u^2_{100}({\bf r_2})] [\uparrow \downarrow − \downarrow \uparrow] \nonumber$

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