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On bound states for systems of weakly coupled Schrödinger equations in one space dimension
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 PhysicsISSN
0022-2488Publisher
American Institute of PhysicsExternal DOI
Issue
11Volume
43Page range
5365-5385Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2013-09-19Usage metrics
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