Explicit diagrammatic solution of normalised, nondegenerate Rayleigh-Schr\"odinger perturbation theory
Quantum Physics
2022-07-20 v2 Mathematical Physics
math.MP
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 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.
Keywords
Cite
@article{arxiv.2105.05009,
title = {Explicit diagrammatic solution of normalised, nondegenerate Rayleigh-Schr\"odinger perturbation theory},
author = {Joel C. Pommerening and David P. DiVincenzo},
journal= {arXiv preprint arXiv:2105.05009},
year = {2022}
}
Comments
version essentially as published (open access), 27 pages, 8 figures