Formal and Precise Derivation of the Green Functions for a Simple Potential

Details Formal and Precise Derivation of the Green Functions for a Simple Potential Formal and Precise Derivation of the Green Functions for a Simple Potential

2001-07-19

arxiv.org/abs/quant-ph/0107096v1

Chaos, Solitons & Fractals 12 (2001) 2689-2695

Physics

Quantum Physics

8 pages, no figures, presented at the second workshop on "Rigged Hilbert Space in Quantum Mechanics" at Clausthal, Germany, 23

Scientific paper

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.

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