On the calculation of irregular solutions of the Schrödinger equation for non-spherical potentials with applications to metallic alloys

IF 1.9 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Frontiers in Physics Pub Date : 2024-07-30 DOI:10.3389/fphy.2024.1393130
Rudolf Zeller
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Abstract

The irregular solutions of the stationary Schrödinger equation are important for the fundamental formal development of scattering theory. They are also necessary for the analytical properties of the Green function, which in practice can greatly speed up calculations. Nevertheless, they are seldom considered in numerical treatments because of their divergent behavior at origin. This divergence demands high numerical precision that is difficult to achieve, particularly for non-spherical potentials which lead to different divergence rates in the coupled angular momentum channels. Based on an unconventional treatment of boundary conditions, an integral-equation method is here developed which is capable of dealing with this problem. The available precision is illustrated by electron-density calculations for NiTi in its monoclinic B19’ structure.
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关于非球形势的薛定谔方程不规则解的计算及其在金属合金中的应用
静态薛定谔方程的不规则解对于散射理论的基本形式发展非常重要。它们对于格林函数的分析特性也是必要的,在实践中可以大大加快计算速度。然而,由于它们在原点处的发散行为,在数值处理中很少考虑它们。这种发散要求很高的数值精度,而这是很难实现的,特别是对于非球面势,因为非球面势会导致耦合角动量通道的发散率不同。本文基于对边界条件的非常规处理,开发了一种能够处理这一问题的积分方程方法。通过对单斜 B19'结构镍钛的电子密度计算,说明了该方法的精确性。
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来源期刊
Frontiers in Physics
Frontiers in Physics Mathematics-Mathematical Physics
CiteScore
4.50
自引率
6.50%
发文量
1215
审稿时长
12 weeks
期刊介绍: Frontiers in Physics publishes rigorously peer-reviewed research across the entire field, from experimental, to computational and theoretical physics. This multidisciplinary open-access journal is at the forefront of disseminating and communicating scientific knowledge and impactful discoveries to researchers, academics, engineers and the public worldwide.
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