Analysis of the Feshbach–Schur method for the Fourier spectral discretizations of Schrödinger operators

Dusson, Geneviève; Sigal, Israel; Stamm, Benjamin

doi:10.1090/mcom/3774

Analysis of the Feshbach–Schur method for the Fourier spectral discretizations of Schrödinger operators
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by Geneviève Dusson, Israel Michael Sigal and Benjamin Stamm;

Math. Comp. 92 (2023), 217-249

DOI: https://doi.org/10.1090/mcom/3774

Published electronically: September 23, 2022

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Abstract:

In this article, we propose a new numerical method and its analysis to solve eigenvalue problems for self-adjoint Schrödinger operators, by combining the Feshbach–Schur perturbation theory with the spectral Fourier discretization. In order to analyze the method, we establish an abstract framework of Feshbach–Schur perturbation theory with minimal regularity assumptions on the potential that is then applied to the setting of the new spectral Fourier discretization method. Finally, we present some numerical results that underline the theoretical findings.

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