000 03223nam a22004935i 4500
001 978-3-642-12248-4
003 DE-He213
005 20160624101836.0
007 cr nn 008mamaa
008 100528s2010 gw | s |||| 0|eng d
020 _a9783642122484
_9978-3-642-12248-4
024 7 _a10.1007/978-3-642-12248-4
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aYserentant, Harry.
_eauthor.
245 1 0 _aRegularity and Approximability of Electronic Wave Functions
_h[electronic resource] /
_cby Harry Yserentant.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aVIII, 188 p. 6 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2000
505 0 _aand 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.
520 _aThe 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.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aNumerical analysis.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aApproximations and Expansions.
650 2 4 _aNumerical Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642122477
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2000
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-12248-4
942 _2EBK1939
_cEBK
999 _c31233
_d31233