In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
Dans cet article, nous donnons dans le régime de perturbation une condition nécessaire et suffisante sur l’existence de valeurs propres plongées entre les deux seuils. Pour une valeur propre de l’opérateur non-perturbé plongée à un seuil, nous démontrons qu’elle peut engendrer à la fois des valeurs propres discrètes et des résonances.
@article{AFST_2007_6_16_1_179_0,
author = {Xue Ping Wang},
title = {Embedded eigenvalues and resonances of {Schr\"odinger} operators with two channels},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {179--214},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 16},
number = {1},
year = {2007},
doi = {10.5802/afst.1144},
mrnumber = {2325597},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1144/}
}
TY - JOUR AU - Xue Ping Wang TI - Embedded eigenvalues and resonances of Schrödinger operators with two channels JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2007 SP - 179 EP - 214 VL - 16 IS - 1 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1144/ DO - 10.5802/afst.1144 LA - en ID - AFST_2007_6_16_1_179_0 ER -
%0 Journal Article %A Xue Ping Wang %T Embedded eigenvalues and resonances of Schrödinger operators with two channels %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2007 %P 179-214 %V 16 %N 1 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1144/ %R 10.5802/afst.1144 %G en %F AFST_2007_6_16_1_179_0
Xue Ping Wang. Embedded eigenvalues and resonances of Schrödinger operators with two channels. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 1, pp. 179-214. doi : 10.5802/afst.1144. https://afst.centre-mersenne.org/articles/10.5802/afst.1144/
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