BriUouin-Wigner perturbation

Reduced Resolvent or the Almosf Inverse of MBPT Machinery Part 1 Energy Equation MBPT Machinery Part 2 Wave Function Equation BriUouin-Wigner Perturbation Theory Rayleigh-Schrodinger Perturbation Theory... 

Let us go back to our problem we want to have Eq on the left side of the last equation, while - for the time being - Eq occurs on the right sides of both equations. To exit the situation, we will treat Eq occurring on the right side as a parameter manipulated in such a way as to obtain equality in both of these equations. We may do it in two ways. One leads to the BriUouin-Wigner perturbation theory, the other to the Rayleigh-Schrddinger perturbation theory. 

As an alternative to BriUouin-Wigner perturbation theory, we may consider Rayleigh-Schrodinger perturbation theory, which is size consistent. In this method, the total energy is computed in a stepwise maimer ... 

The use of BriUouin-Wigner perturbation theory in describing many-body systems is critically re-examined. 

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]. 

We will consider first the least problematic of the disadvantages of the BriUouin-Wigner perturbation theory and then the major negative feature of the theory in the modelling of many-body systems. 

The use of BriUouin-Wigner perturbation theory in describing many-body systems has been critically re-examined in recent years [69-96]. It has been shown that under certain well-defined circumstances, it can be regarded as a valid many-body theory. The primary purpose of this volume is to provide a detailed and coherent account of the Brillouin-Wigner methods in the study of the many-body problem in atomic and molecular quantum mechanics. 

In the discussion given in the previous subsection, we have specified the wave operator f by means of the multi-reference BriUouin-Wigner perturbation expansion defined by eqs. (4.59) and (4.60) ... 

BriUouin-Wigner perturbation theory Rayleigh-Schrodinger perturbation theory A = 0-----------------------------= 1 A = 1 ------------A = 0... 

The papers by Lennard-Jones, by BriUouin and by Wigner represent the genesis of what is now termed Brillouin-Wigner perturbation theory . 

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