 04310 David Damanik, Rowan Killip, Barry Simon
 Schr\"odinger Operators With Few Bound States
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Sep 28, 04

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Abstract. We show that wholeline 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 twodimensional Schr\"odinger operators, $H$, with bounded positive ground states: Given a potential $V$, if both $H\pm V$ are bounded from below by the groundstate energy of $H$, then $V\equiv 0$.
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