N-body薛定谔进化方程的混合规律性和稀疏网格近似值
Mixed regularity and sparse grid approximations of N-body Schrödinger evolution equation
Long Meng and Dexuan Zhou
arXiv
2025年9月13日
在本文中,我们提出了对时间依赖的N体电子系统的数学分析,并为相应的波函数建立了混合规律性。 基于此,我们开发稀疏网格近似值,以减少计算复杂性,包括稀疏网格高斯型轨道(GTO)方案。 我们验证了氦原子(He)和氢分子(H_2)的方法,表明稀疏网格GTO为全网格离散提供了一种有效的替代方案。
In this paper, we present a mathematical analysis of time-dependent N-body electronic systems and establish mixed regularity for the corresponding wavefunctions. Based on this, we develop sparse grid approximations to reduce computational complexity, including a sparse grid Gaussian-type orbital (GTO) scheme. We validate the approach on the Helium atom (He) and Hydrogen molecule (H_2), showing that sparse grid GTOs offer an efficient alternative to full grid discretizations.