Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models

Details Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models

2010-06-07

arxiv.org/abs/1006.1372v1

Physics

Mathematical Physics

20 pages

Scientific paper

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of the continuous spectrum and we analyze the effect of various type of perturbations on the spectral singularities. We provide algorithms to obtain convergent series expansions for the coordinates of the singularities.

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