Schrödinger operator with a strong varying interaction on a curve in R2

In this paper, we study a two-dimensional quantum system governed by the Hamiltonian corresponding to the formal expression −Δ−(α+ω(·))δ(·−Γ), where α > 0, ω(·) is a continuous compactly supported function and Γ is a curve in R2. We derive the asymptotics of eigenvalues for α→∞ and analyze consequences of introducing varying delta potential