论文标题
排名一个由混合几何形状支持的扰动及其变形
Rank One Perturbations Supported by Hybrid Geometries and Their Deformations
论文作者
论文摘要
我们研究了$ \ mathbb {r}^2 $和$ \ mathbb {r}^3 $中的等级的混合类型，其中一个圆/球支持的扰动与圆圈/球体外部的指向支撑。明确给出了与圈子和一个点支持的等级的形式表达式相关的自我支持的哈密顿操作员，并明确给出了一个扰动。还研究了每个问题的结合状态能量和散射特性。最后，我们考虑了一个由变形的圆/球支持的等级的扰动，并表明在圆/球的小变形下，界面能量的一阶变化具有简单的几何解释。最后，我们考虑了变形圆/球支持的三角洲电势，并表明在圆/球的小变形下，结合状态能的一阶变化具有简单的几何解释。
We study the hybrid type of rank one perturbations in $\mathbb{R}^2$ and $\mathbb{R}^3$, where the perturbation supported by a circle/sphere is considered together with the delta potential supported by a point outside of the circle/sphere. The construction of the self-adjoint Hamiltonian operator associated with the formal expressions for the rank one perturbation supported by a circle and by a point is explicitly given. The bound state energies and scattering properties for each problem are also studied. Finally, we consider the rank one perturbation supported by a deformed circle/sphere and show that the first order change in the bound state energies under small deformations of the circle/sphere has a simple geometric interpretation. Finally, we consider the delta potentials supported by deformed circle/sphere and show that the first order change in the bound state energies under small deformations of circle/sphere has a simple geometric interpretation.
