Remarks on the Complexity of the Schrödinger Equation

Yserentant, Harry

doi:doi:10.1063/1.3498475

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AIP Conference Proceedings / Volume 1281

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Remarks on the Complexity of the Schrödinger Equation

AIP Conf. Proc. 1281, pp. 35-37; doi:http://dx.doi.org/10.1063/1.3498475 (3 pages)

ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010

Date: 19–25 September 2010

Location: Rhodes (Greece)

Harry Yserentant

Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany

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The solutions of the electronic Schrödinger equation are high‐dimensional objects depending on 3N variables, three for each of the N electrons under consideration. It is therefore rather surprising that simple expansions of the electronic wave functions can be constructed whose convergence rate, measured in terms of the number of determinants involved, is independent of the number of electrons and does not fall below that for a two‐ or even that for a one‐electron system approximated in the same way. In this sense, the complexity of the electronic Schrödinger equation does not exceed that of an equation in three space dimensions. A short report on these developments is given.