Genealogical coupling scheme

We give in this section an introduction to the construction of CSFs and more generally to the construction of spin tensor operators. We shall employ the genealogical coupling scheme, where the final CSF for N electrons is arrived at in a sequence of N steps [2]. At each step, a new electron is introduced and coupled to those already present. We thus arrive at the final CSF through a sequence of N —I intermediate CSFs, each of which represents a spin eigenfunction. 

In the genealogical scheme, we envisage each //-electron state [t) as arising by a coupling of the one-body alpha and beta creation operators with a spin-adapted (N — 1 )-electron state ... 

In this exercise, we use the genealogical scheme to couple the tensor operators a pp] and —Oqp, aqa) to Obtain spin-adapted one-electron operators. 

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