A new partitioning technique for the calculation of Bloch's wave operators

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Abstract
A new algorithm, involving the Bloch wave operator theory, is applied to the eigenvalue problem in large vectorial spaces. Three subspaces constituting the whole Hilbert space are then defined: the space of the trial eigenvector, an intermediate space comprising the states strongly coupled to the latter and a complementary space of large size. In the two former defined spaces each of the components of the Bloch wave operator associated with the eigenvector is separately calculated by using both procedures of standard diagonalization and of iterative perturbation. The relationship between the projections of the wave operator onto these two subspaces is deduced from a recursive scheme. The resonance state of the Henon-Heiles potential with E and A symmetry illustrate the adequacy of the formulation.