论文标题
在半线上的单数Schrödinger操作员的特征
A characterization of singular Schrödinger operators on the half-line
论文作者
论文摘要
我们研究了一类Laplacian在半线上的Delta样扰动，其特征在于起源处的Robin边界条件。使用非标准分析的形式主义，我们与合适的Schrödinger运算符家族得出了一个简单的联系，其潜力非常大（无限）幅度且非常短（无穷小）范围。结果，在径向电势的情况下，我们还获得了欧几里得空间$ \ mathbb {r}^3 $的点相互作用的类似结果。此外，我们在原点附近有线性的情况下明确讨论了我们的结果。
We study a class of delta-like perturbations of the Laplacian on the half-line, characterized by Robin boundary conditions at the origin. Using the formalism of nonstandard analysis, we derive a simple connection with a suitable family of Schrödinger operators with potentials of very large (infinite) magnitude and very short (infinitesimal) range. As a consequence, we also derive a similar result for point interactions in the Euclidean space $\mathbb{R}^3$, in the case of radial potentials. Moreover, we discuss explicitly our results in the case of potentials that are linear in a neighbourhood of the origin.
