Overview
- The style is excellent and pedagogical
- The author is first class analyst
- Accessible to a mathematical audience at the beginning graduate level as well as to physicists and theoretical chemists with a comparable mathematical background
- The contents requires no deeper knowledge of the theory of partial differential equations, of functional analysis, or quantum theory
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2000)
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About this book
The electronic Schrodi ¨ nger equation describes the motion of N electrons under Coulomb interaction forces in a eld of clamped nuclei. Solutions of this equation depend on 3N variables, three spatial dimensions for each electron. Approxim- ing the solutions is thus inordinately challenging, and it is conventionally believed that a reduction to simpli ed models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to c- vince the reader 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 present notes arose from lectures that I gave in Berlin during the academic year 2008/09 to introduce beginning graduate students of mathematics into this subject. They are kept on an intermediate level that should be accessible to an audience of this kind as well as to physicists and theoretical chemists with a c- responding mathematical training.
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Reviews
From the reviews:
“This monograph discusses the possible direct approximation of the wavefunction itself, in view of several nice properties of the functions at hand (spatial exponential decay, symmetries, regularity, etc.). … the book is very pleasant to read, having been written very carefully, and with many proofs provided explicitly. The text should be understandable to any graduate student in (applied) mathematics, as well as students and researchers from chemistry and physics … .” (Gabriel Stoltz, Mathematical Reviews, Issue 2011 d)Authors and Affiliations
Bibliographic Information
Book Title: Regularity and Approximability of Electronic Wave Functions
Authors: Harry Yserentant
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-642-12248-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Softcover ISBN: 978-3-642-12247-7Published: 04 June 2010
eBook ISBN: 978-3-642-12248-4Published: 19 May 2010
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 188
Number of Illustrations: 6 b/w illustrations
Topics: Partial Differential Equations, Approximations and Expansions, Numerical Analysis