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arXiv · 2304.14995

Majorana transformation of the Thomas-Fermi equation demystified

Abdaljalel Alizzi·Zurab K. Silagadze
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Abstract

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.

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Abdaljalel Alizzi, Zurab K. Silagadze. 2023-04-08. Majorana transformation of the Thomas-Fermi equation demystified. https://doi.org/10.1142/s0217732324500160

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