


Abstract
Harry Yserentant, Thu, 16.3017.20

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Sparse grids, hyberbolic cross spaces, and the regularity of the Schrödinger equation
Harry Yserentant (Uni Tübingen)
The electronic Schrödinger equation describes the
motion of electrons under Coulomb interaction forces
in the field of clamped nuclei and forms the basis of
quantum chemistry. The talk is concerned with the
regularity properties of the corresponding
wavefunctions that are compatible with the Pauli
principle, both in spatial and momentum
representation. It is shown that these solutions
possess certain square integrable mixed weak
derivatives of order up to N+1 with N the
number of electrons. The result mathematically
substantiates approximation methods that are based on
the idea of sparse grids or hyperbolic cross spaces.
It lets expect that such schemes represent a
promising alternative to current methods for the
solution of the electronic Schrödinger equation and
that it could even become possible to reduce the
computational complexity of an Nelectron problem
to that of a oneelectron problem.




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