Two simple eigenfunctions of the spin

Consider an n electron system in a pure spin state S. The associated partition is n/2 + S,n/2 — S], and the first standard tableau is 

The spin raising operator (see Eq. (4.3)) may now be applied to this result, and we obtain 

We now investigate the behavior of 0 when we apply our two simple Hermitian idempotents discussed earlier. 

Since 5 + and both commute with ff and V, both pnp and npn are eigenfunctions of the operator with total spin S and Ms = S. 

Heretofore in this section we have been working with the partition A, = n/2 + S, n/2 — 5, but references to it in the equations have been suppressed. We now write 

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