  In formal scattering theory, Green functions are obtained as solutions of a
distributional equation. In this paper, we use the Sturm-Liouville theory to
compute Green functions within a rigorous mathematical theory. We shall show
that both the Sturm-Liouville theory and the formal treatment yield the same
Green functions. We shall also show how the analyticity of the Green functions
as functions of the energy keeps track of the so-called ``incoming'' and
``outgoing'' boundary conditions.
