Lennard-Jones-Brillouin-Wigner perturbation theory

Lennard-Jones Brillouin Wigner Perturbation Theory.—Let us write the total hamiltonian operator as a sum of a zero-order operator and a perturbation... 

In Lennard-Jones Brillouin Wigner perturbation theory the wave operator is written as... 

The Rayleigh-Schrodinger peiturbation theory can be derived from the Lennard-Jones-Brillouin-Wigner perturbation theory by expanding the energy-dependent denominators which occur in the latter... 

J. E. Lennard-Jones [37]. (Indeed, some authors [38,39] refer to the method as Lennard-Jones-Brillouin-Wigner perturbation theory .) Subsequently, L. Brillouin published his famous paper in 1932 [40] whilst E.P. Wigner s paper appeared some 2 years later [41]. In this section, we provide a brief synopsis of each of these important papers. 

As we have noted already, some authors, such as Dalgarno [38] and Wilson [39], term what is nowadays called Brillouin-Wigner perturbation theory Lennard-Jones-Brillouin-Wigner perturbation theory in recognition of the seminal contribution of Sir John Lennard-Jones. 

Rayleigh-Schrodinger Perturbation Theory.—In Rayleigh-Schrodinger perturbation theory the unknown energy in the denominators of the Lennard-Jones Brillouin Wigner expansion is avoided. This enables a size-consistent theory to be derived. 

The seminal paper on what is nowadays called Brillouin-Wigner perturbation theory by Lennard-Jones was published in the Proceedings of the Royal Society of London in 1931. It was communicated by R.H. Fowler and received on 1st September, 1930. Here we reproduce Lennard-Jones introduction ... 

Wigner s contribution to Brillouin-Wigner perturbation theory appeared some 2 years after Brillouin s paper in 1935. It was published in Mathematischer und Naturwissenschaftlicher Anzeiger der Ungarischen Akademie der Wi -senschaften. Wigner cites the earlier work of Brillouin but not that of Lennard-Jones. The first part of Wigner s paper is in Hungarian ... 

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

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. 

This advantage of the Brillouin-Wigner perturbation theory was recognized in the original papers by Lennard-Jones [37] and of Brillouin [40]. It is also described in the review by Dalgarno [38]. 

The perturbation theory of Lennard-Jones, Brillouin, and Wigner is not size consistent. 

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