Non-hermitian nature of the degenerate hypergeometric equation

Abstract

With an explicit expression for the Green's function, Eq. (19), we have a common method for obtaining the radial parts of the Green's functions for a broad range of physical problems which lead to the Whittaker equation (listed in part in the introduction). This analysis emphasizes the special role played by the Whittaker equation in physical applications. Since the symmetry of the Green's function — an important property — is a consequence of the self-adjoint nature of the corresponding differential operator, the Whittaker equation is apparently the most general second-order equation with one regular singularity and one irregular singularity which retains its value for inhomogeneous physical problems, i.e., for problems leading to inhomogeneous differential equations.