Embedded eigenvalues and resonances of Schrödinger operators with two channels

Xue Ping Wang[1]

  • [1] Département de Mathématiques, UMR 6629 CNRS, Université de Nantes, 44322 Nantes Cedex France

Annales de la faculté des sciences de Toulouse Mathématiques (2007)

  • Volume: 16, Issue: 1, page 179-214
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Wang, Xue Ping. "Embedded eigenvalues and resonances of Schrödinger operators with two channels." Annales de la faculté des sciences de Toulouse Mathématiques 16.1 (2007): 179-214. <http://eudml.org/doc/10030>.

@article{Wang2007,
abstract = {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.},
affiliation = {Département de Mathématiques, UMR 6629 CNRS, Université de Nantes, 44322 Nantes Cedex France},
author = {Wang, Xue Ping},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
number = {1},
pages = {179-214},
publisher = {Université Paul Sabatier, Toulouse},
title = {Embedded eigenvalues and resonances of Schrödinger operators with two channels},
url = {http://eudml.org/doc/10030},
volume = {16},
year = {2007},
}

TY - JOUR
AU - Wang, Xue Ping
TI - Embedded eigenvalues and resonances of Schrödinger operators with two channels
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2007
PB - Université Paul Sabatier, Toulouse
VL - 16
IS - 1
SP - 179
EP - 214
AB - 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.
LA - eng
UR - http://eudml.org/doc/10030
ER -

References

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