- 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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