Fund Quantum Mechanics Lect & HW Solutions 95

Fund Quantum Mechanics Lect & HW Solutions 95 -...

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5.9. HEAVIER ATOMS 77 eigenfunction ψ 1 = ψ S 1 has, according to its deFnition above, both electrons spin-up and in the excited antisymmetric spatial state ( ψ l ψ r ψ r ψ l ) / 2. A similar guess that works is ( a 1 , a 2 , a 3 , a 4 ) = (0 , 0 , 0 , 1) . This corresponds to the eigenfunction ψ 2 = ψ S 4 in which both electrons are spin-down, and again in the antisymmetric spatial state. The third one that works is ( a 1 , a 2 , a 3 , a 4 ) = (0 , 1 , 1 , 0) / 2 where the scale factor 2 is only needed to ensure that the vector is of unit length. The eigenstate ψ 3 = ( ψ S 2 + ψ S 3 ) / 2 corresponds, according to the deFnitions of ψ S 2 and ψ S 3 above, to the electrons being in the antisymmetric spatial state times the
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