论文标题
软量子层的绑定状态
Bound states in soft quantum layers
论文作者
论文摘要
我们开发了一种一般方法来研究具有限制电势的三维Schroedinger操作员，具体取决于到达表面的距离。主要思想是根据表面施加平行坐标，但在欧几里得空间中的切割基因座之外。如果表面在适当的意义上是渐近的平面，我们就会对Schroedinger操作员必需光谱的位置进行估计。此外，如果表面与严格的总高斯曲率与革命的表面相吻合，则表明Schroedinger操作员具有无限数量的离散特征值。
We develop a general approach to study three-dimensional Schroedinger operators with confining potentials depending on the distance to a surface. The main idea is to apply parallel coordinates based on the surface but outside its cut locus in the Euclidean space. If the surface is asymptotically planar in a suitable sense, we give an estimate on the location of the essential spectrum of the Schroedinger operator. Moreover, if the surface coincides up to a compact subset with a surface of revolution with strictly positive total Gauss curvature, it is shown that the Schroedinger operator possesses an infinite number of discrete eigenvalues.
