Harry Yserentant (TU Berlin)

Title: The regularity of electronic wave functions in Barron spaces
Abstract: The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. It is fundamental to our understanding of chemistry. The solutions of this equation, the electronic wave functions, are high-dimensional objects. They depend on 3N variables, three associated with the position of each of the N electrons in space. Inspired by the extensive recent work on the approximation properties of neural networks, the talk deals with the regularity of these wave functions in Barron spaces. It is shown that they lie in the spectral Barron spaces B^s(ℝ^3N ) for s < 1. The example of the hydrogen ground state shows that this result cannot be improved.
(Host: Markus Bachmayr)