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Introduction and Outline

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2000)

Abstract

The approximation of high-dimensional functions, whether they be given explicitly or implicitly as solutions of differential equations, represents one of the grand challenges of applied mathematics. High-dimensional problems arise in many fields of application such as data analysis and statistics, but first of all in the sciences. One of the most notorious and complicated problems of this type is the Schrödinger equation. The Schrödinger equation forms the basis of quantum mechanics and is of fundamental importance for our understanding of atoms and molecules. It links chemistry to physics and describes a system of electrons and nuclei that interact by Coulomb attraction and repulsion forces. As proposed by Born and Oppenheimer in the nascency of quantum mechanics, the slower motion of the nuclei is mostly separated from that of the electrons.

Keywords

  • Essential Spectrum
  • Electronic Wave Function
  • Sparse Grid
  • Pauli Principle
  • Hyperbolic Cross

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Harry Yserentant .

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© 2010 Springer Berlin Heidelberg

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Yserentant, H. (2010). Introduction and Outline. In: Regularity and Approximability of Electronic Wave Functions. Lecture Notes in Mathematics(), vol 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12248-4_1

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