Size-extensivity of exponential wave functions

The great difficulties faced by the linear model in representing noninteracting fragments in a compact manner suggest that we should consider alternative models for the wave function, where the separability of the wave function is built into the ansatz itself. Specifically, we shall in this subsection advocate the use of exponential wave functions as a natural ansatz for separable approximate wave functions. 

We begin our discussion by writing the exact wave operators for the noninteracting fragments in the exponential form 

From Section 4.3.1, we know that the exact wave operator for the compound system is given by the product of and ij B- In the exponential representation, this product wave function becomes 

in this particular representation, the compound wave function for the noninteracting fragments is generated by the sum of the excitation operators for the individual systems  

This situation should be contrasted with the linear variation method, where the wave operators for 

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