# Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 6, page 1337-1362
- ISSN: 0764-583X

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topBachmayr, Markus. "Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1337-1362. <http://eudml.org/doc/277843>.

@article{Bachmayr2012,

abstract = {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.},

author = {Bachmayr, Markus},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Schrödinger equation; mixed regularity; transcorrelated method; wavelets; separable approximation; error estimate; molecular system; Galerkin method; eigenvalue problem},

language = {eng},

month = {3},

number = {6},

pages = {1337-1362},

publisher = {EDP Sciences},

title = {Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation},

url = {http://eudml.org/doc/277843},

volume = {46},

year = {2012},

}

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

DA - 2012/3//

PB - EDP Sciences

VL - 46

IS - 6

SP - 1337

EP - 1362

AB - 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.

LA - eng

KW - Schrödinger equation; mixed regularity; transcorrelated method; wavelets; separable approximation; error estimate; molecular system; Galerkin method; eigenvalue problem

UR - http://eudml.org/doc/277843

ER -

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