On quantum waveguide with shrinking potential
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🧮 math-ph
math.MP
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eigenvaluespotentialshrinkingspectrumasymptoticconditionsconsiderconstruct
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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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