Schroedinger Operators With Few Bound States

Details Schroedinger Operators With Few Bound States Schroedinger Operators With Few Bound States

2004-09-28

arxiv.org/abs/math-ph/0409074v2

Physics

Mathematical Physics

10 pages

Scientific paper

10.1007/s00220-005-1366-x

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 $V\equiv 0$.

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