General scheme of splittings of degenerate eigensubspaces and eigenelements of self-adjoint operators in high orders of perturbation theory

The possibility of arbitrary alternation of splitting and nonsplitting orders is taken into consideration through the idea of a stage of perturbation theory. In every order an eigenvalue equation is to be solved; its effective operator is obtained by means of a unified scheme from the operator of th...

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Bibliographic Details
Published in:Journal of mathematical physics 2000-08, Vol.41 (8), p.5793-5813
Main Authors: Tsaune, A. Ya, Dyachenko, M. P.
Format: Article
Language:English
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Summary:The possibility of arbitrary alternation of splitting and nonsplitting orders is taken into consideration through the idea of a stage of perturbation theory. In every order an eigenvalue equation is to be solved; its effective operator is obtained by means of a unified scheme from the operator of the previous order. The complete aggregate of subspace splittings leads to the correct set of eigenvectors of zero approximation. Expressions of any order corrections for the correct vectors leading to eigenvectors of a perturbed operator are obtained and discussed.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.533438