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On quantum waveguide with shrinking potential

We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the sufficient conditions for such eigenvalues to emerge. If such eigenvalues exist, we construct their asymptotic expansions.

preprint2009arXivOpen access
A. BikmetovR. Gadyl'shin
math-phmath.MP
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A. BikmetovR. Gadyl'shin

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