In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue problem based on orthogonal wavelets are described, and possible choices of tensor product bases are compared especially from an algorithmic point of view. The use of separable approximations of potential terms for applying operators efficiently is studied in detail, and estimates for the error due to this further approximation are given.
Mots-clés : Schrödinger equation, mixed regularity, transcorrelated method, wavelets, separable approximation
@article{M2AN_2012__46_6_1337_0,
author = {Bachmayr, Markus},
title = {Hyperbolic wavelet discretization of the two-electron {Schr\"odinger} equation in an explicitly correlated formulation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1337--1362},
publisher = {EDP-Sciences},
volume = {46},
number = {6},
year = {2012},
doi = {10.1051/m2an/2012009},
mrnumber = {2996330},
zbl = {1276.65075},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2012009/}
}
TY - JOUR AU - Bachmayr, Markus TI - Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 1337 EP - 1362 VL - 46 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012009/ DO - 10.1051/m2an/2012009 LA - en ID - M2AN_2012__46_6_1337_0 ER -
%0 Journal Article %A Bachmayr, Markus %T Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1337-1362 %V 46 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012009/ %R 10.1051/m2an/2012009 %G en %F M2AN_2012__46_6_1337_0
Bachmayr, Markus. Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 1337-1362. doi : 10.1051/m2an/2012009. http://www.numdam.org/articles/10.1051/m2an/2012009/
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