Explicit formula for perturbation theory at any order with infinitely many perturbations
Abstract
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that contains the information for both the eigenvalue and eigenvector corrections. The formula reduces to the standard case of one perturbation in the appropriate limit. This formulation streamlines the derivations that are traditionally tedious in perturbation theory, facilitating high-order calculations.
Fields of Study & Subjects
Mathematical functions and polynomials
Quantum chaos and dynamical systems
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Physical review. B./Physical review. B
- Publisher
- American Physical Society (APS)
- Volume
- 113
- Issue
- 11
- Publication date
- 24 February 2026
- Language
- EN