The electronic Schrödinger equation describes the motion of N-electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, with three spatial dimensions for each electron. Approximating these solutions is thus inordinately challenging, and it is generally believed that a reduction to simplified models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to show readers that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons. The text is accessible to a mathematical audience at the beginning graduate level as well as to physicists and theoretical chemists with a comparable mathematical background and requires no deeper knowledge of the theory of partial differential equations, functional analysis, or quantum theory.

Bibliographic references

Includes bibliographical references and index.

Contents

And Outline

Fourier Analysis

The Basics of Quantum Mechanics

The Electronic Schrödinger Equation

Spectrum and Exponential Decay

Existence and Decay of Mixed Derivatives

Eigenfunction Expansions

Convergence Rates and Complexity Bounds

The Radial-Angular Decomposition.

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Other format(s)

Also available in an electronic version.

In

Springer eBooks

ISBN

3642122477

9783642122477

9783642122484

3642122485

LCCN

2010927755

OCLC

639164953

Doi

10.1007/978-3-642-12248-4

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