Analytic properties of the scattering matrix

Summary

The discussion of the behaviour of theS-matrix is here carried out on the basis of the modern theory of entire analitic functions (1) forS waves and for a spinless particle scattered by a fixed spherical potential. It is shown that many of the properties of Jost’sf (k) functions can be derived quite rigorously and simply, from very general theorems. Among them we point out a theorem on the existence of infinite zeros off(k) when the potential decreases fast enough as to make f(k) regular in the whole plane ofk. The asymptotic behaviour of the distribution of these zeros is also discussed.

Riassunto

Le proprietà délia funzione di Jost sono derivate usando noti risultati delia teoria delie funzioni intere. In particolare l’andamento asintotico dei grandi zeri di detta funzione è discusso nei dettagli.