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Rational approximation to the Thomas-Fermi equations
Authors:Francisco M Fernández
Institution:INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata, Argentina
Abstract:We show that a simple and straightforward rational approximation to the Thomas-Fermi equation provides the slope at origin with unprecedented accuracy and that Padé approximants of relatively low order are far more accurate than more elaborate approaches proposed recently by other authors. We consider both the Thomas-Fermi equation for isolated atoms and for atoms in strong magnetic fields.
Keywords:Thomas-Fermi equation  Isolated atoms  Atoms in magnetic fields  Rational approximation  Padé  approximants  Hankel determinants
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