Majorana transformation of the Thomas-Fermi equation demystified
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914742672556032 |
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| author | Alizzi, Abdaljalel Silagadze, Zurab K. |
| author_facet | Alizzi, Abdaljalel Silagadze, Zurab K. |
| contents | The Majorana transformation makes it possible to reduce the Thomas-Fermi equation to a first-order differential equation. This reduction is possible due to the special scaling property of the Thomas-Fermi equation under homology transformations. Such reductions are well known in the context of stellar astrophysics, where the use of homology-invariant variables has long proved useful. We use homology-invariant variables in the context of the Thomas-Fermi equation to demystify the origin of the otherwise mysterious Majorana transformation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_14995 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Majorana transformation of the Thomas-Fermi equation demystified Alizzi, Abdaljalel Silagadze, Zurab K. Analysis of PDEs High Energy Physics - Phenomenology History and Philosophy of Physics The Majorana transformation makes it possible to reduce the Thomas-Fermi equation to a first-order differential equation. This reduction is possible due to the special scaling property of the Thomas-Fermi equation under homology transformations. Such reductions are well known in the context of stellar astrophysics, where the use of homology-invariant variables has long proved useful. We use homology-invariant variables in the context of the Thomas-Fermi equation to demystify the origin of the otherwise mysterious Majorana transformation. |
| title | Majorana transformation of the Thomas-Fermi equation demystified |
| topic | Analysis of PDEs High Energy Physics - Phenomenology History and Philosophy of Physics |
| url | https://arxiv.org/abs/2304.14995 |