The R-Matrix Problem

Equations (11.24) can be solved using the second quantization expression for He given by (11.23). They are identical to the eqs. (8.76) for the phonon VV problem, but with fermion operators c ci instead of boson operators a ai. However, the operators ci also form a closed set with respect to commutations and the algebraic problem is therefore identical to the one for bosons, i.e., we have 

This also implies that states below or above the Fermi level are coupled only through the higher-order terms obtained when exponentiating the matrix. For 

FIGURE 11.3 A state below the Fermi level is excited to a state above. The matrix element connected to this transition is Hij and it is induced by the operator c/cj.  

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