Explicit diagrammatic solution of normalised, nondegenerate Rayleigh-Schr\"odinger perturbation theory

• URL: http://arxiv.org/abs/2105.05009v2
• Date: Tue, 15 Feb 2022 11:34:59 GMT
• Title: Explicit diagrammatic solution of normalised, nondegenerate Rayleigh-Schr\"odinger perturbation theory
• Authors: Joel C. Pommerening, David P. DiVincenzo
• Abstract summary: We solve the coupled recurrence relations for eigenenergies and -vectors in nondegenerate Rayleigh-Schr"odinger theory. The series can be expressed in terms of diagrams that were first introduced by C. Bloch.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We solve the coupled recurrence relations for eigenenergies and -vectors in nondegenerate Rayleigh-Schr\"odinger perturbation theory under the constraint that the approximate eigenvector be normalised to $1$ 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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