Mixed regularity and sparse grid approximations of $N$-body Schrödinger evolution equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909788150956032 |
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| author | Meng, Long Zhou, Dexuan |
| author_facet | Meng, Long Zhou, Dexuan |
| contents | 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 (${\rm H}_2$), showing that sparse grid GTOs offer an efficient alternative to full grid discretizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed regularity and sparse grid approximations of $N$-body Schrödinger evolution equation Meng, Long Zhou, Dexuan Numerical Analysis Mathematical Physics Analysis of PDEs Atomic Physics Computational Physics 35J10, 35B65, 41A25, 41A63 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 (${\rm H}_2$), showing that sparse grid GTOs offer an efficient alternative to full grid discretizations. |
| title | Mixed regularity and sparse grid approximations of $N$-body Schrödinger evolution equation |
| topic | Numerical Analysis Mathematical Physics Analysis of PDEs Atomic Physics Computational Physics 35J10, 35B65, 41A25, 41A63 |
| url | https://arxiv.org/abs/2509.10805 |