On radial Schrödinger operators with a Coulomb potential: general boundary conditions

This paper presents the spectral analysis of 1-dimensional Schro ̈dinger operator onthe half-line whose potential is a linear combination of theCoulomb term1/randthecentrifugal term1=r2. The coupling constants are allowed to be complex, and allpossible boundary conditions at 0 are considered. The resulting closed operators areorganized in three holomorphic families. These operators are closely related to theWhittaker equation. Solutions of this equation are thoroughly studied in a largeappendix to this paper. Various special cases of this equation are analyzed, namelythedegenerate, theLaguerreand thedoubly degeneratecases. A new solution to theWhittaker equation in the doubly degenerate case is also introduced.