Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 6, p. 1337-1362

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.

DOI : https://doi.org/10.1051/m2an/2012009
Classification:  35B65,  35J10,  65T60,  81Q05
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {6},
     year = {2012},
     pages = {1337-1362},
     doi = {10.1051/m2an/2012009},
     zbl = {1276.65075},
     mrnumber = {2996330},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 6, pp. 1337-1362. doi : 10.1051/m2an/2012009. http://www.numdam.org/item/M2AN_2012__46_6_1337_0/

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