Bound states due to a strong δ interaction supported by a curved surface
نویسندگان
چکیده
We study the Schrödinger operator −∆ − αδ(x − Γ) in L2(R3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if Γ is asymptotically planar in a suitable sense and α > 0 is sufficiently large this operator has a non-empty discrete spectrum and derive an asymptotic expansion of the eigenvalues in terms of a “two-dimensional” comparison operator determined by the geometry of the surface Γ.
منابع مشابه
ar X iv : m at h - ph / 0 20 70 25 v 2 1 4 N ov 2 00 2 Bound states due to a strong δ interaction supported by a curved surface
We study the Schrödinger operator −∆ − αδ(x − Γ) in L 2 (R 3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if Γ is asymptotically planar in a suitable sense and α > 0 is sufficiently large this operator has a non-empty discrete spectrum and derive an asymptotic expansion...
متن کاملar X iv : m at h - ph / 0 20 70 25 v 1 1 9 Ju l 2 00 2 Bound states due to a strong δ interaction supported by a curved surface
We study the Schrödinger operator −∆ − αδ(x − Γ) in L 2 (R 3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth, admits a global normal parameterization, and is asymptotically planar in a suitable sense. We show that for a large enough α > 0 this operator has a non-empty discrete spectrum and derive an asymptotic expansion of the eigenvalues in terms of a " two-...
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