Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1899181 | Reports on Mathematical Physics | 2016 | 17 Pages |
Abstract
We consider Schrödinger operators with a strongly attractive singular interaction supported by a finite curve Γ of length L in ℝ3. We show that if Γ is C4-smooth and has regular endpoints, the j -th eigenvalue of such an operator has the asymptotic expansion λj(Hα,Γ)=ξα+λj(S)+O(eπα)λj(Hα,Γ)=ξα+λj(S)+O(eπα) as the coupling parameter α → -∞, where ξα = −4e2(−2πα+ψ(1)) and λj(S) is the j -th eigenvalue of the Schrödinger operator S=−d2ds2−14γ2(s)on L2(0, L) with Dirichlet condition at the interval endpoints in which γ is the curvature of Γ.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Pavel Exner, Sylwia Kondej,