Majorana transformation of the Thomas-Fermi equation demystified
arXiv:2304.14995 · doi:10.1142/S0217732324500160
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.
8 pages, no figures, published version