Premium
Using symbolic computing in building probabilistic models for atoms
Author(s) -
Guiasu Silviu
Publication year - 2005
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.20745
Subject(s) - probabilistic logic , formalism (music) , wave function , atom (system on chip) , beryllium , hydrogen atom , statistical physics , computer science , physics , quantum mechanics , group (periodic table) , artificial intelligence , art , musical , nuclear physics , visual arts , embedded system
This article shows how symbolic computing and the mathematical formalism induced by maximizing entropy and minimizing the mean deviation from statistical equilibrium may be effectively applied to obtaining probabilistic models for the structure of atoms, using trial wave functions compatible with an average shell picture of the atom. The objective is not only to recover the experimental value of the ground state mean energy of the atom, but rather to better approximate the unknown parameters of these trial functions and to calculate both correlations between electrons and the amount of interdependence among different subsets of electrons of the atoms. The examples and numerical results refer to the hydrogen, helium, lithium, and beryllium atoms. The main computer programs, using the symbolic computing software MATHEMATICA, are also given. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006