Abstract
We solve the coupled recurrence relations for eigenenergies and -vectors in nondegenerate Rayleigh-Schrödinger perturbation theory under the constraint that the approximate eigenvector be normalised to in every order. The series can be expressed in terms of diagrams that were first introduced by C. Bloch [Nucl. Phys. 6, 329 (1958)] for the degenerate, unnormalised case. Normalisation increases the number of terms and introduces a nontrivial dependence on the diagrams' topology to the coefficients.
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