Advantages of the Brillouin-Wigner theory

We consider the advantages of the Brillouin-Wigner perturbation theory on the basis of the elementary derivations given in Sections 1.3.1 and 1.3.2. 

Brillouin-Wigner perturbation theory has five main advantages over the Rayleigh-Schrodinger perturbation theory. These are  

This perspective on Brillouin-Wigner perturbation theory was mentioned by Lennard-Jones in his seminal 1930 paper [37]. It was also described in the review byDalgarno [38] published in 1961. 

Consider, for example, the second-order energy,, in the Brillouin-Wigner perturbation expansion for the ground state energy. From the third term on the right-hand side of eq. (1.17), we see that this may be written in sum-over-states form as 

The relative simplicity of Brillouin-Wigner perturbation theory was noted by Wigner in his original publication [41]. The simplicity of BriUouin-Wigner perturbation theory was emphasized by Dalgarno in his review [38]. 

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