R. de la Madrid
Formal and Precise Derivation of the Green Functions for a Simple
Potential
(22K, latex)
ABSTRACT. 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.