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arXiv · 2308.10996

Perturbation-based Non-perturbative Method

Chang Liu·Wen-Du Li·Wu-Sheng Dai
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Abstract

This paper presents a nonperturbative method for solving eigenproblems. This method applies to almost all potentials and provides nonperturbative approximations for any energy level. The method converts an eigenproblem into a perturbation problem, obtains perturbation solutions through standard perturbation theory, and then analytically continues the perturbative solution into a nonperturbative solution. Concretely, we follow three main steps: (1) Introduce an auxiliary potential that can be solved exactly and treat the potential to be solved as a perturbation on this auxiliary system. (2) Use perturbation theory to obtain an approximate polynomial of the eigenproblem. (3) Use a rational approximation to analytically continue this approximate polynomial into the nonperturbative region.

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Chang Liu, Wen-Du Li, Wu-Sheng Dai. 2023-07-25. Perturbation-based Non-perturbative Method. https://doi.org/10.1016/j.aop.2024.169741

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