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On bound states for systems of weakly coupled Schrödinger equations in one space dimension

journal contribution
posted on 2023-06-08, 15:51 authored by Michael MelgaardMichael Melgaard
We establish the Birman–Schwinger relation for a class of Schrödinger operators -d2/dx2?1H+V on L2(math,H), where H is an auxiliary Hilbert space and V is an operator-valued potential. As an application we give an asymptotic formula for the bound states which may arise for a weakly coupled Schrödinger operator with a matrix potential (having one or more thresholds). In addition, for a two-channel system with eigenvalues embedded in the continuous spectrum we show that, under a small perturbation, such eigenvalues turn into resonances

History

Publication status

  • Published

Journal

Journal of Mathematical Physics

ISSN

0022-2488

Publisher

American Institute of Physics

Issue

11

Volume

43

Page range

5365-5385

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-09-19

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