Strong coupling asymptotics for a singular Schrödinger operator with an interaction supported by an open arc
نویسندگان
چکیده
We consider a singular Schrödinger operator in L(R) written formally as −∆ − βδ(x − γ) where γ is a C smooth open arc in R of length L with regular ends. It is shown that the jth negative eigenvalue of this operator behaves in the strong-coupling limit, β → +∞, asymptotically as Ej(β) = − β 4 + μj +O ( log β β ) , where μj is the jth Dirichlet eigenvalue of the operator − d 2 ds2 − κ(s) 2 4 on L(0, L) with κ(s) being the signed curvature of γ at the point s ∈ (0, L).
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