We review recent results on the semiclassical behaviour of Schrödinger operators with Neumann boundary conditions. In this setting, the validity of Weyl’s law requires additional conditions on the potential. We will explain the techniques needed to control the number of bound states near the boundary, thus leading to universal estimates on the number of bound states.
@article{SLSEDP_2022-2023____A3_0,
author = {Charlotte Dietze},
title = {Weyl{\textquoteright}s law for {Neumann} {Schr\"odinger} operators on {H\"older} domains},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:9},
pages = {1--9},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2022-2023},
doi = {10.5802/slsedp.158},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.158/}
}
TY - JOUR AU - Charlotte Dietze TI - Weyl’s law for Neumann Schrödinger operators on Hölder domains JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:9 PY - 2022-2023 SP - 1 EP - 9 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.158/ DO - 10.5802/slsedp.158 LA - en ID - SLSEDP_2022-2023____A3_0 ER -
%0 Journal Article %A Charlotte Dietze %T Weyl’s law for Neumann Schrödinger operators on Hölder domains %J Séminaire Laurent Schwartz — EDP et applications %Z talk:9 %D 2022-2023 %P 1-9 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.158/ %R 10.5802/slsedp.158 %G en %F SLSEDP_2022-2023____A3_0
Charlotte Dietze. Weyl’s law for Neumann Schrödinger operators on Hölder domains. Séminaire Laurent Schwartz — EDP et applications (2022-2023), Talk no. 9, 9 p. doi : 10.5802/slsedp.158. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.158/
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