[Etat fondamental de l'opérateur de Schrödinger avec champ magnétique dans un domaine à coin]
Nous démontrons que la réalisation de Neumann de l'opérateur de Schrödinger avec un champ magnétique constant sur un secteur
We show that the Neumann realization for the Schrödinger operator with a constant magnetic field in a sector has at least one eigenvalue below the essential spectrum, when the angle is sufficiently small. We establish the complete asymptotics of the lowest eigenvalue as the angle tends to 0. This study is applied to the analysis of the bottom of the spectrum in the semi-classical case for domains with edges.
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Virginie Bonnaillie 1
@article{CRMATH_2003__336_2_135_0, author = {Virginie Bonnaillie}, title = {On the fundamental state for a {Schr\"odinger} operator with magnetic field in a domain with corners}, journal = {Comptes Rendus. Math\'ematique}, pages = {135--140}, publisher = {Elsevier}, volume = {336}, number = {2}, year = {2003}, doi = {10.1016/S1631-073X(03)00008-6}, language = {en}, }
TY - JOUR AU - Virginie Bonnaillie TI - On the fundamental state for a Schrödinger operator with magnetic field in a domain with corners JO - Comptes Rendus. Mathématique PY - 2003 SP - 135 EP - 140 VL - 336 IS - 2 PB - Elsevier DO - 10.1016/S1631-073X(03)00008-6 LA - en ID - CRMATH_2003__336_2_135_0 ER -
Virginie Bonnaillie. On the fundamental state for a Schrödinger operator with magnetic field in a domain with corners. Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 135-140. doi : 10.1016/S1631-073X(03)00008-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00008-6/
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