Size Consistency Problem in the Energy

To gain some experience in the evaluation of perturbation contributions to j and Ej and to motivate an analysis of a fundamental weakness of the Buillouin-Wigner perturbation theory (BWPT), let us now consider a few examples. First, we evaluate the first-order correction to the energy that arises from the n = 0 term in Eq. (3.11)  

Note that because E contains no reference to the parameter RSPT and BWPT have identical first-order energies. 

we consider the second-order energy and, in particular, we examine for a system consisting of two noninteracting subsystems a and h). For this case, the Hamiltonian // separates into 

The second-order energy expression from Eq. (3.11) reduces, using Q j = 0, to 

Expressing Q in the conventional sum-over-states manner gives 

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