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Sparse grid spaces for the numerical solution of the electronic Schrödinger equation

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Abstract

This article complements the author’s recent work [Numer. Math. 98, 731–759 (2004)] on the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives. It has been shown there that the solutions of this equation are surprisingly smooth and possess square integrable mixed weak derivatives of order up to N+1 with N the number of electrons across the singularities of the interaction potentials, and it has been claimed that this result can help to break the complexity barriers in computational quantum mechanics using correspondingly antisymmetrized sparse grid trial functions. A construction of this kind that can be interpreted as a sparse grid sampling theorem is sketched here.

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  1. Institut für Mathematik, TU Berlin, 10623, Berlin, Germany

    H. Yserentant

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Yserentant, H. Sparse grid spaces for the numerical solution of the electronic Schrödinger equation. Numer. Math. 101, 381–389 (2005). https://doi.org/10.1007/s00211-005-0581-x

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