Article ID Journal Published Year Pages File Type
1899181 Reports on Mathematical Physics 2016 17 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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