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A change of variable for the perturbation parameter in rayleigh–Schrödinger perturbation theory
Author(s) -
Amos A. T.
Publication year - 1972
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560060109
Subject(s) - perturbation (astronomy) , poincaré–lindstedt method , scaling , perturbation theory (quantum mechanics) , physics , møller–plesset perturbation theory , singular perturbation , mathematical physics , quantum mechanics , mathematics , geometry
The Feenberg–Goldhammer change of scale, whereby the H 0 in perturbation theory is replaced by (1/μ) H 0 with μ a scaling parameter, is shown to be equivalent to a change of variable for the perturbation parameter. A more general change of variable is shown to lead to a perturbation series with perturbation energies E 3 , …, E 2n+1 equal to zero. The resulting energy through (2 n + 1)th order has the same form as that found from the Brillouin–Wigner series by different methods.