TY - JOUR

T1 - Majorana transformation of the Thomas-Fermi equation demystified

AU - Alizzi, Abdaljalel

AU - Silagadze, Zurab K.

PY - 2024/3/7

Y1 - 2024/3/7

N2 - The Majorana transformation makes it possible to reduce the Thomas-Fermi equation to a firstorder di®erential 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.

AB - The Majorana transformation makes it possible to reduce the Thomas-Fermi equation to a firstorder di®erential 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.

KW - Emden-Fowler equation

KW - Lane-Emden equation

KW - Majorana transformation

KW - Thomas-Fermi equation

KW - homology-invariant variables

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85189478210&origin=inward&txGid=2f7d6b5acd8524a04857f18d97f498ff

UR - https://www.mendeley.com/catalogue/480105c0-76ca-3e65-b9f9-1266b7ff2b5c/

U2 - 10.1142/S0217732324500160

DO - 10.1142/S0217732324500160

M3 - Article

VL - 39

JO - Modern Physics Letters A

JF - Modern Physics Letters A

SN - 0217-7323

IS - 7

M1 - 2450016

ER -