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Variational solution of the Thomas‐Fermi equation for compressed atoms at high temperatures
Author(s) -
Csavinszky P.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560180816
Subject(s) - work (physics) , atom (system on chip) , variational method , function (biology) , fermi gamma ray space telescope , physics , thomas–fermi model , constant (computer programming) , quantum mechanics , atomic physics , electron , evolutionary biology , computer science , programming language , biology , embedded system
The purpose of the present work is to show that the temperature‐perturbed Thomas‐Fermi (TF) equation of Marshak and Bethe may be solved approximately for compressed neutral atoms by formulating two variational principles. One variational principle is formulated for obtaining an approximate analytical solution ϕ 0 of the TF equation for a compressed atom at T = 0 K, and another one for obtaining an approximate analytical correction function θ In terms of these quantities the approximate finite‐temperature solution of the TF equation is given by ϕ T = ϕ 0 + (T/θ) 2 θ, where θ is a constant depending on the atomic number Z.