论文标题
在具有库仑电势的径向Schroedinger操作员上：一般边界条件
On radial Schroedinger operators with a Coulomb potential: General boundary conditions
论文作者
论文摘要
本文介绍了一维Schroedinger操作员的光谱分析，其潜在的是库仑项1/r和离心项1/r^2的线性组合。允许耦合常数是复杂的，并且考虑了0处的所有可能边界条件。由此产生的封闭操作员在三个全态家庭中组织。这些操作员与惠特克方程密切相关。该方程的解决方案在本文的大型附录中进行了详尽的研究。分析了该方程的各种特殊情况，即退化，拉瓜和双重变性病例。还引入了双重变性案例中惠特克方程的新解决方案。
This paper presents the spectral analysis of 1-dimensional Schroedinger operator on the half-line whose potential is a linear combination of the Coulomb term 1/r and the centrifugal term 1/r^2. The coupling constants are allowed to be complex, and all possible boundary conditions at 0 are considered. The resulting closed operators are organized in three holomorphic families. These operators are closely related to the Whittaker equation. Solutions of this equation are thoroughly studied in a large appendix to this paper. Various special cases of this equation are analyzed, namely the degenerate, the Laguerre and the doubly degenerate cases. A new solution to the Whittaker equation in the doubly degenerate case is also introduced.
