Iterative process for solving Hartree-Fock equations by means of a wavelet transform
type: Item
instance of: scholarly article
title: Iterative process for solving Hartree-Fock equations by means of a wavelet transform
zbMATH Open document ID: 0804.65118
author: Patrick Armin Fischer
author: Mireille Defranceschi
published in: Applied and Computational Harmonic Analysis
publication date: 1995-01-04T00:00:00Z
review text: The Hartree-Fock equation (HF) for the hydrogen atom \(F_ i \varphi_ i (X) = ( - {1 \over 2} \Delta (x) + V(X)) \varphi_ i (X) = \varepsilon_ i \varphi_ i (X)\) is analyzed by means of the continuous wavelet transform to show how to improve the Gaussian approximation by an iterative process. The one-dimensional space is treated, studying only the radial dependence of the wave function. Then the wavelet transform of the HF operator is performed and an iterative scheme is defined in position -- momentum space. The first iterate is obtained analytically with a Gaussian function defined as the initial guess. The problem of the singularity for \(x=0\) of the HF equation is bypassed. The improvement by the first iteration is assessed by comparison with the transform of the Slater function. The wavelet transforms are shown and analyzed.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35A22
Mathematics Subject Classification ID: 81V45
zbMATH DE Number: 626002
zbMATH Keywords: Hartree-Fock equation
zbMATH Keywords: hydrogen atom
zbMATH Keywords: wavelet transform
zbMATH Keywords: Gaussian approximation
zbMATH Keywords: iterative process
zbMATH Keywords: singularity
zbMATH Keywords: Slater function
MaRDI profile type: Publication
full work available at URL: acha.1994.1010
OpenAlex ID: W2087867572
DOI: 10.1006/ACHA.1994.1010
description: scientific article; zbMATH DE number 626002