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 orde rs is taken into consideration through the idea of a stage of perturbation theory. In every order an eigenvalue equation is to be solved; its effectiv e operator is obtained by means of a unified scheme from the operator of th e previous order. The complete aggregate of subspace splittings leads to th e correct set of eigenvectors of zero approximation. Expressions of any ord er corrections for the correct vectors leading to eigenvectors of a perturb ed operator are obtained and discussed. (C) 2000 American Institute of Phys ics. [S0022-2488(00)03504-0].