95-280 Simon B.
Some Schr\"odinger Operators with Dense Point Spectrum (17K, AMSTeX) Jun 15, 95
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Abstract. Given any sequence $\{E_n\}^\infty_{n-1}$ of positive energies and any monotone function $g(r)$ on $(0,\infty)$ with $g(0)=1$, $\lim\limits_{r\to\infty} g(r)=\infty$, we can find a potential $V(x)$ on $(-\infty,\infty)$ so that $\{E_n\}^\infty_{n=1}$ are eigenvalues of $-\frac{d^2}{dx^2}+V(x)$ and $|V(x)|\leq (|x|+1)^{-1} g(|x|)$.

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