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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.29482 |
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| _version_ | 1866915952595042304 |
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| author | Englert, Berthold-Georg |
| author_facet | Englert, Berthold-Georg |
| contents | Majorana found a way to exploit the scaling properties of the Thomas-Fermi equation for converting this second-order differential equation into one of first order. We explore his method for the familiar neutral-atom solution and extend it to the solution that is relevant for weakly ionized atoms. Various integrals and other quantities with importance for atomic physics are recalculated and their values compared with the ones obtained in the 1980s by more tedious numerical procedures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29482 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thomas-Fermi equation revisited: A variation on a theme by Majorana Englert, Berthold-Georg Atomic Physics Classical Analysis and ODEs Computational Physics 34A05, 35Q99, 53C29, 81V45 Majorana found a way to exploit the scaling properties of the Thomas-Fermi equation for converting this second-order differential equation into one of first order. We explore his method for the familiar neutral-atom solution and extend it to the solution that is relevant for weakly ionized atoms. Various integrals and other quantities with importance for atomic physics are recalculated and their values compared with the ones obtained in the 1980s by more tedious numerical procedures. |
| title | Thomas-Fermi equation revisited: A variation on a theme by Majorana |
| topic | Atomic Physics Classical Analysis and ODEs Computational Physics 34A05, 35Q99, 53C29, 81V45 |
| url | https://arxiv.org/abs/2603.29482 |