Bound States Due to a Strong Interaction Supported By a Curved Surface

We study the Schrödinger operator #) in ) with a delta interaction supported by an infinite non-planar surface Gamma which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if Gamma is asymptotically planar in a suitable sense and alpha > 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 Gamma.

Hali tarjima qilinmagan