Regularity of many-body Schrödinger evolution equation and its application to numerical analysis
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866911159846699008 |
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| author | Meng, Long |
| author_facet | Meng, Long |
| contents | A decade ago, the mixed regularity of stationary many-body Schrö\-dinger equation has been studied by Harry Yserentant through the Pauli Principle and the Hardy inequality (Uncertainty Principle). In this article, we prove that the many-body evolution Schrödinger equation has a similar mixed regularity if the initial data $u_0$ satisfies the Pauli Principle. By generalization of the Strichartz estimates, our method also applies to the numerical approximation of this problem: based on these mixed derivatives, we design a new approximation which can hugely improve the computing capability especially in quantum chemistry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_02274 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Regularity of many-body Schrödinger evolution equation and its application to numerical analysis Meng, Long Analysis of PDEs A decade ago, the mixed regularity of stationary many-body Schrö\-dinger equation has been studied by Harry Yserentant through the Pauli Principle and the Hardy inequality (Uncertainty Principle). In this article, we prove that the many-body evolution Schrödinger equation has a similar mixed regularity if the initial data $u_0$ satisfies the Pauli Principle. By generalization of the Strichartz estimates, our method also applies to the numerical approximation of this problem: based on these mixed derivatives, we design a new approximation which can hugely improve the computing capability especially in quantum chemistry. |
| title | Regularity of many-body Schrödinger evolution equation and its application to numerical analysis |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1803.02274 |