AUTHORS: Toby D. Young

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ABSTRACT: This contribution presents the numerical analysis of Hartree-Fock’s method of computing electron atomic statefunctions using Galerkin’s finite element method. The underlying theory and computational implementation are presented in some detail for the first time and highly accurate energies are presented for free neutral atoms, ions, and for the spatially confined He atom. The method of using local basis sets is shown to be competitive with global basis sets of the Slater and modified Slater types in terms of accuracy and use.

KEYWORDS: Atomic physics, Finite element method, Numerical analysis, Quantum confinement

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