Schr{<$}dinger算子Fourier谱离散的Feshbach-Schur方法分析
Analysis of the Feshbach-Schur method for the Fourier Spectral discretizations of Schr{ö}dinger operators
摘要：
本文将Feshbach-Schur扰动理论与谱Fourier离散相结合，提出了一种求解自伴Schr{}dinger算子本征值问题的新的数值方法及其分析.为了分析该方法，我们建立了一个抽象的框架Feshbach-Schur扰动理论的最小正则性假设的潜力，然后应用到设置新的频谱傅立叶离散方法。最后，我们提出了一些数值结果，强调的理论研究结果。
英文摘要：
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.
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