lecture32figs - ~ o-J.~ vy ~cif 118 and ~ ~ u~ "J'-...

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~ o-J.~~ vy ~cif 118 and This means that the correct eigenfunctions of 82 and S: are "7> and The S == 0 function is just the singlet spin state analogous to what we the ground state of He, while the S = 1 state is of triplet multiplicity. for the triplet, the electrpns can have m s = 1/l for both electrons, -1 "- or a symmetric mixture of +1/2 and -1/2. U we now form the linear combinations"'3 :!: 1/1'" of Eqs. (8.32), we the space and spin parts may be factored. The spin parts are the singlet ~ wavefunctions just defined, Furthermore, the space part of the triplet same as for I/J1 and 1/12' This means that we can group the excited states 4 the singlet state 1 "'sirJ&)et Z(al~ - .B1a2X4>ls(1)~(2) + cf>2.(1)~,(2» ~ and the three triplets 1 t/1trip1et ,. Vi [Ml)~(2} - ~(1)~1I(2)] . Both the singlet and triplet states are consistent with the Pauli princip spatial part of the singlet state is symmetric with respect to interch~ electrons, while the spatial part of the triplet state is antisymmetric. . ferences are important in determining the relative energies of the si
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lecture32figs - ~ o-J.~ vy ~cif 118 and ~ ~ u~ "J'-...

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