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Mini-workshop on "Mathematical and numerical challenges in quantum chemistry"
Organizers: Claude Le Bris (Paris, France) & Christian Lubich (Tuebingen, Germany)


Harry Yserentant (Berlin, Germany): "On the approximability of electronic wavefunctions: regularity and behind"
Monday 24 June 2013, 16:40 - 17:20
Amphi Darboux


The eigenfunctions of electronic Schr"odinger operators and their exponentially weighted counterparts possess, roughly speaking, mixed weak derivatives of fractional order θ for
θ<3/4 in the Sobolev space H1. The bound 3/4 is best possible and can neither be reached nor surpassed. Such results are important for the study of sparse grid-like expansions of the wave functions and show that their asymptotic convergence rate measured in terms of the number of ansatz functions involved does not deteriorate with the number of electrons. The resulting rate of convergence (not to speak of the actually reachable speed of convergence) is, however, low. The question arises which other properties of the wavefunctions, and what kind of nonlinear approximation methods as well, could help to improve this situation.