Resolvent, Rayleigh-Schrodinger

In these expressions, fR is the Rayleigh-Schrodinger resolvent for the ground state, which can be written in sum-over-states form as... 

To make further progress, we introduce the Rayleigh-Schrodinger resolvent. 

The Rayleigh-Schrodinger resolvent In Rayleigh-Schrodinger perturbation theory the resolvent is defined by... 

An alternative approach, which we shall follow in this work, is to solve eqs. (4.145) and (4.146), which define the much simpler Brillouin-Wigner scheme, and introduce a correction term for the non-linear effects. The following identity relates the Brillouin-Wigner and the Rayleigh-Schrodinger resolvent denominators [17,18,74]... 

In order to develop the Rayleigh-Schrodinger perturbation expansion for the energy and the wave function, we define the resolvent... 

Elimination of the size-extensivity error in the MRBWCC theory was suggested by Hubac and Wilson [68]. The Brillouin-Wigner perturbation theory has been known notoriously as a method not furnishing size extensivity. There was therefore every reason to believe that the size-extensivity error in MR BWCCSD originated from the use of the Brillouin-Wigner type resolvent (15) instead of the Rayleigh-Schrodinger... 

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... 

The effective Hamiltonian (2.88) can be written in terms of the resolvent IRo for Rayleigh-Schrodinger perturbation theory as... 

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