Mixed regularity and sparse grid approximations of N-body Schrödinger evolution equation

2025/09/13 by Long Meng, Meng, Long, Dexuan Zhou +1
Earth and Planetary Sciences · Mathematics · #35B65 #35J10 #41A25 #41A63 #Analysis of PDEs (math.AP) #Arctic and Antarctic ice dynamics #Atomic Physics (physics.atom-ph) #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2509.10805

openalex publication_date 2025/09/13 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

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 (\rm He) and Hydrogen molecule (\rm H₂), showing that sparse grid GTOs offer an efficient alternative to full grid discretizations.

Citations

• Exploring the attosecond laser-driven electron dynamics in the hydrogen molecule with different real-time time-dependent configuration interaction approaches
• Existence and regularity of propagators for multi-particle Schrödinger equations in external fields

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