On radial Schroedinger operators with a Coulomb potential: General boundary conditions

Abstract: 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.