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# Scattering Length and the Spectrum of $-\Delta+V$

Published:2006-03-01
Printed: Mar 2006
• Michael Taylor
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## Abstract

Given a non-negative, locally integrable function $V$ on $\RR^n$, we give a necessary and sufficient condition that $-\Delta+V$ have purely discrete spectrum, in terms of the scattering length of $V$ restricted to boxes.