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

@article{Melgaard2002OnBS,
  title={On bound states for systems of weakly coupled Schr{\"o}dinger equations in one space dimension},
  author={Michael Melgaard},
  journal={Journal of Mathematical Physics},
  year={2002},
  volume={43},
  pages={5365-5385}
}
  • M. Melgaard
  • Published 21 October 2002
  • Mathematics
  • Journal of Mathematical Physics
We establish the Birman–Schwinger relation for a class of Schrodinger operators −d2/dx2⊗1H+V on L2(R,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 Schrodinger 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… 
2 Citations
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  • Physics, Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2002
Results are obtained on perturbation of eigenvalues and half-bound states (zero-resonances) embedded at a threshold. The results are obtained in a two-channel framework for small off-diagonal
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