论文标题
用于Schr {Ö} Dinger Operators傅立叶光谱离散化的Feshbach-Schur方法的分析
Analysis of the Feshbach-Schur method for the Fourier Spectral discretizations of Schr{ö}dinger operators
论文作者
论文摘要
在本文中，我们提出了一种新的数值方法及其分析，以通过将Feshbach-Schur扰动理论与光谱傅立叶离散化相结合，以解决自动化schr {Ö} dinger操作员的特征值问题。为了分析该方法，我们建立了Feshbach-Schur扰动理论的抽象框架，其规律性假设最少，然后将其应用于新频谱傅立叶离散方法的设置。最后，我们提出了一些强调理论发现的数值结果。
In this article, we propose a new numerical method and its analysis to solve eigenvalue problems for self-adjoint Schr{ö}dinger 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.
