A Canonical Gauge for Computing of Eigenpairs of the Magnetic Schrödinger Operator

Jeffrey S. Ovall, Li Zhu
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Abstract

We consider the eigenvalue problem for the magnetic Schr\"odinger operator and take advantage of a property called gauge invariance to transform the given problem into an equivalent problem that is more amenable to numerical approximation. More specifically, we propose a canonical magnetic gauge that can be computed by solving a Poisson problem, that yields a new operator having the same spectrum but eigenvectors that are less oscillatory. Extensive numerical tests demonstrate that accurate computation of eigenpairs can be done more efficiently and stably with the canonical magnetic gauge.
计算磁薛定谔算子特征对的典型量纲
我们考虑了磁性薛定谔算子的特征值问题,并利用一种称为量规不变性的性质,将给定的问题转化为一个更适于数值逼近的等效问题。更具体地说,我们提出了一个可以通过求解泊松问题来计算的典型磁规,它产生了一个具有相同频谱但特征向量振荡较小的新算子。广泛的数值测试表明,使用规范磁规可以更高效、更稳定地计算特征对。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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