Large-order perturbation theory of linear eigenvalue problems

Journal article

Abstract:: We consider a class of linear eigenvalue problems depending on a small parameter ϵ in which the series expansion for the eigenvalue in powers of ϵ is divergent. We develop a new technique to determine the precise nature of this divergence. We illustrate the technique through its application to four examples: the anharmonic oscillator, a simplified model of equatorially-trapped Rossby waves, and two simplified models based on quasinormal modes of Reissner–Nordström–de Sitter black holes.

Files:: Chapman_2026_Large-order_perturbation_theory.pdf

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Publisher:: Royal Society
Journal:: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences More from this journal
Volume:: 482
Issue:: 2334
Article number:: 20250813
Publication date:: 2026-03-25
Acceptance date:: 2026-02-03
DOI:: 10.1098/rspa.2025.0813
EISSN:: 1471-2946
ISSN:: 1364-5021

Language:: English
Keywords:: exponential asymptotics

Stokes phenomenon

divergent expansion

WKB theory

quantum mechanics
Pubs id:: 2366502
Local pid:: pubs:2366502
Deposit date:: 2026-02-03
ARK identifier:: ark:/29072/ora_44d3045e1a494760a5d2bd2d8ebb353f

Copyright holder:: S. Jonathan Chapman
Rights statement:: © 2026 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

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