X iv : m at h - ph / 0 10 60 25 v 1 2 5 Ju n 20 01 Band gap of the Schrödinger operator with a strong δ - interaction on a periodic curve
نویسنده
چکیده
In this paper we study the operator Hβ = −∆− βδ(· − Γ) in L2(R2), where Γ is a smooth periodic curve in R2. We obtain the asymptotic form of the band spectrum of Hβ as β tends to infinity. Furthermore, we prove the existence of the band gap of σ(Hβ) for sufficiently large β > 0. Finally, we also derive the spectral behaviour for β → ∞ in the case when Γ is non-periodic and asymptotically straight.
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تاریخ انتشار 2001