On the nature of the large-$q$ expansion of the response for a non-relativistic confined system

Abstract

We show the equivalence of a previously derived exact expression for the response of a non-relativistic system with harmonic forces and an infinite sum of weighted $\delta$-functions corresponding to the spectrum. We forward arguments, indicating that the Gersch-Rodriguez-Smith $1/q$-expansion of the response does not converge and prove that this expansion is an asymptotic series.

Comments: 8 pages, appended ps file for figs, report no's INFN-ISS 93/9; WIS-93/71/Nov-PH