Analysis of the Feshbach-Schur method for the Fourier Spectral discretizations of Schrödinger operators

Geneviève Dusson (1) , Israel Michael Sigal , Benjamin Stamm (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 RWTH - Rheinisch-Westfälische Technische Hochschule Aachen University

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.

Domaines: Analyse numérique [math.NA]

Geneviève Dusson, Israel Michael Sigal, Benjamin Stamm. Analysis of the Feshbach-Schur method for the Fourier Spectral discretizations of Schrödinger operators. Mathematics of Computation, 2023, ⟨10.1090/mcom/3774⟩. ⟨hal-02919770v2⟩