- 04-310 David Damanik, Rowan Killip, Barry Simon
- Schr\"odinger Operators With Few Bound States
Sep 28, 04
(auto. generated ps),
of related papers
Abstract. We show that whole-line Schr\"odinger operators with finitely many bound states have no embedded singular spectrum. In contradistinction, we show that embedded singular spectrum is possible even when the bound states approach the essential spectrum exponentially fast.
We also prove the following result for one- and two-dimensional Schr\"odinger operators, $H$, with bounded positive ground states: Given a potential $V$, if both $H\pm V$ are bounded from below by the ground-state energy of $H$, then $V\equiv 0$.