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Study of the convergence radius of the Rayleigh–Schrödinger perturbation series for the delta‐function model of H 2 +
Author(s) -
Claverie Pierre
Publication year - 1969
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.560030309
Subject(s) - radius of convergence , perturbation (astronomy) , radius , convergence (economics) , upper and lower bounds , series (stratigraphy) , function (biology) , physics , nucleus , mathematical physics , mathematical analysis , rayleigh scattering , bound state , charge (physics) , mathematics , quantum mechanics , power series , paleontology , computer security , evolutionary biology , computer science , microbiology and biotechnology , economics , biology , economic growth
The convergence radius of the series expansion for the energy of H 2 + in the δ‐function model (in terms of the perturbation parameter μ/λ, where μ is the charge of the perturbing nucleus and λ the fixed charge of the other nucleus) is investigated. A lower bound of this convergence radius (possibly equal to it) previously defined by Robinson [5] is studied analytically as a function of the internuclear distance R and computed numerically. The results differ strikingly from those previously obtained by Robinson who used a simplified but poorer lower bound: in contrast with this poorer bound, the one studied in the present paper is larger than for I every R , from which fact it may be concluded that, contrary to Robinson's previous result, the series expansion of the energy, in the δ‐function model under consideration, still converges when μ = λ for every R .