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Some Schrödinger operators with dense point spectrum
Authors:Barry Simon
Institution:Division of Physics, Mathematics, and Astronomy, California Institute of Technology, 253-37, Pasadena, California 91125
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 $(-\infty ,\infty )$ such 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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