 9719 Christian Remling
 Some Schr\"odinger operators with powerdecaying potentials and
pure point spectrum
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Jan 14, 97

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Abstract. We construct deterministic (= nonrandom) potentials $V(x)=O(x^{c})$
such that the onedimensional Schr\"odinger equation $y''+Vy=Ey$
on the halfaxis $x\in [0,\infty)$ has dense pure point spectrum
in $(0,\infty)$ for almost all boundary conditions at $x=0$.
A modification of this construction yields powerdecaying potentials
for which the spectrum is purely singular continuous in $(0,\infty)$
for all boundary conditions.
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