| Issue |
ESAIM: M2AN
Volume 60, Number 2, March-April 2026
|
|
|---|---|---|
| Page(s) | 689 - 699 | |
| DOI | https://doi.org/10.1051/m2an/2026015 | |
| Published online | 09 April 2026 | |
The regularity of electronic wave functions in barron spaces
Technische Universität Berlin, Institut für Mathematik, 10623 Berlin, Germany
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
13
February
2025
Accepted:
8
February
2026
Abstract
The electronic Schrödinger equation describes the motion of a finite number of electrons under Coulomb interaction forces in the field of a finite number of clamped nuclei. It is proved that its solutions for negative eigenvalues, below the essential spectrum, lie in the spectral Barron spaces ℬs for s < 1. Examples show that this limit generally cannot be reached or surpassed.
Mathematics Subject Classification: 35J10 / 35B65 / 68T07
Key words: Schrödinger equation / regularity / Barron spaces
© The authors. Published by EDP Sciences, SMAI 2026
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