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130626  eng 
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a 9783642122484

100 
1 

a Yserentant, Harry

245 
0 
0 
a Regularity and Approximability of Electronic Wave Functions
h Elektronische Ressource
c by Harry Yserentant

250 


a 1st ed. 2010

260 


a Berlin, Heidelberg
b Springer Berlin Heidelberg
c 2010, 2010

300 


a VIII, 188 p. 6 illus
b online resource

505 
0 

a 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 RadialAngular Decomposition

653 


a Approximations and Expansions

653 


a Partial Differential Equations

653 


a Numerical analysis

653 


a Numerical Analysis

653 


a Partial differential equations

653 


a Approximation theory

041 
0 
7 
a eng
2 ISO 6392

989 


b Springer
a Springer eBooks 2005

490 
0 

a Lecture Notes in Mathematics

856 
4 
0 
u https://doi.org/10.1007/9783642122484?nosfx=y
x Verlag
3 Volltext

082 
0 

a 515.353

520 


a The electronic Schrödinger equation describes the motion of Nelectrons 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 HartreeFock 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
