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T:A:L:K:S
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title:
Regularity, complexity, and approximability of electronic wavefunctions |
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name:
Yserentant |
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first name:
Harry
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location/conference:
SPP-JT09
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PRESENTATION-link:
http://dfg-spp1324.de/download/jt09/talks/yserentant.pdf |
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abstract:
This talk considers the electronic Schrödinger equation of quantum theory that
describes the motion of N electrons under Coulomb interaction forces in a field
of clamped nuclei. Solutions of this equation depend on 3N variables, three spatial
dimensions for each electron. Approximating the solutions is thus inordinately
challenging, and it is conventionally believed that a reduction to simplified
models, such as those of the Hartree-Fock method or density functional theory,
is the only tenable approach. We indicate why 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 only two electrons. Some very recent results on the approximation
by wavelets and on the decomposition into angular momentum
eigenfunction are described. |
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