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19th GAMM-Seminar Leipzig on
High-dimensional problems - Numerical treatment and applications

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999


     
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  19th GAMM-Seminar
January, 23th-25th, 2003
 
     
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  Abstract Harry Yserentant, Thu, 16.30-17.20 Previous Contents Next  
  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 N-electron problem to that of a one-electron problem.
 

 
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