On quantum waveguide with shrinking potential

Details On quantum waveguide with shrinking potential On quantum waveguide with shrinking potential

2009-09-28

arxiv.org/abs/0909.5115v1

Physics

Mathematical Physics

Scientific paper

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.

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