In this article, we propose a new numerical method and its analysis to solve eigenvalue problems for self-adjoint Schr{\"o}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.

翻译：在文章中,我们提出一种新的数字方法及其分析方法,通过将Feshbach-Schur 扰动理论与光谱 Fourier 分解法相结合,解决自联Schr\"o}dinger 操作员的基因价值问题。为了分析这个方法,我们建立了一个Feshbach-Schur 扰动理论的抽象框架,同时对新光谱Fourier 分解法的设定适用的可能性作出最起码的规律性假设。最后,我们提出了一些数字结果,以强调理论结论。