论文标题
量子图：库仑型电势和准确可解决的模型
Quantum graphs: Coulomb-type potentials and exactly solvable models
论文作者
论文摘要
我们在非紧密的星形图上研究了Schrödinger运算符，其库仑型电势在顶点处具有奇异性。正规化的汉密尔顿人$ h_ \ varepsilon $与截止库仑电势以及$（αδ+βδ'）$的临界值 - 研究了1D库仑电位和$Δ'$ - 电位对其正常化方法非常敏感。建立了$ h_ \ varepsilon $的规范分解收敛条件，具体取决于正规化。汉密尔顿人的极限为Schrödinger的运营商提供了库仑型电位在数学上精确的含义，从而确保了正确选择顶点条件。我们还描述了星形图上正式库仑汉密尔顿人的所有自我参与实现。
We study the Schrödinger operators on a non-compact star graph with the Coulomb-type potentials having singularities at the vertex. The convergence of regularized Hamiltonians $H_\varepsilon$ with cut-off Coulomb potentials coupled with $(αδ+βδ')$-like ones is investigated.The 1D Coulomb potential and the $δ'$-potential are very sensitive to their regularization method. The conditions of the norm resolvent convergence of $H_\varepsilon$ depending on the regularization are established. The limit Hamiltonians give the Schrödinger operators with the Coulomb-type potentials a mathematically precise meaning, ensuring the correct choice of vertex conditions. We also describe all self-adjoint realizations of the formal Coulomb Hamiltonians on the star graph.
