Dependence of Perturbation Expansions

1 The N-dependence of perturbation expansions. - Historically, there appeared two distinct approaches to perturbation theory for quantum systems - that associated with the names of Lennard-Jones,86 Brillouin87 and Wigne88 

For the unperturbed model system, the Schrodinger equation may be written 

The perturbation expansion of Lennard-Jones,86 Brillouin87 and Wigner88 is obtained from (19) by making a Taylor expansion in powers of X 

The Rayleigh-Schrodinger perturbation series is obtaining by applying Go (is) from the left to equation (15) after re-writing it in the form 

Substituting (26) into (21) gives an expansion for the energy correction E 

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